Chapter 5, Exponents and Polynomials Video Solutions, Elementary and Intermediate Algebra 5th

Section 5

Adding and Subtracting Polynomials

00:33

Problem 1

$\left(b^{3}-b^{2}-9 b+1\right)+\left(b^{3}-b^{2}-9 b+1\right)$ is the sum of two ________.

Julie S.

Numerade Educator

00:33

Problem 2

$\left(b^{2}-9 b+11\right)-\left(4 b^{2}-14 b\right)$ is the _______ of a trinomial and a binomial.

Julie S.

Numerade Educator

00:18

Problem 3

_________ terms have the same variables with the same exponents.

Julie S.

Numerade Educator

00:45

Problem 4

The polynomial $2 t^{4}+3 t^{3}-4 t^{2}+5 t-6$ is written in _______ powers of $t$

Julie S.

Numerade Educator

00:18

Problem 5

To add polynomials, ________ their like terms.

Julie S.

Numerade Educator

00:31

Problem 6

To subtract polynomials, ______ the signs of the terms of the polynomial being subtracted, drop parentheses, and combine like terms.

Julie S.

Numerade Educator

02:08

Problem 7

Simplify each polynomial, if possible.
a. $2 x^{2}+3 x^{2}$
b. $15 m^{3}-m^{3}$
c. $8 a^{3} b-a^{3} b$
d. $6 c d+4 c^{2} d$

Julie S.

Numerade Educator

00:41

Problem 8

What is the result of the addition in the $x$ -column?
$$
\begin{array}{l}
{4 x^{2}+x-12} \\
{5 x^{2}-8 x+23} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:29

Problem 9

Write without parentheses.
a. $-\left(5 x^{2}-8 x+23\right)$
b. $-\left(-5 y^{4}+3 y^{2}-7\right)$

Julie S.

Numerade Educator

00:44

Problem 10

What is the result of the subtraction in the $x$ -column?
$$
\begin{array}{rl}
{8 x^{2}-7 x-1} & {8 x^{2}-7 x-1} \\
{-\left(4 x^{2}+6 x-9\right)} & {-4 x^{2}-6 x+9} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:30

Fill in the blanks to add (subtract) the polynomials.
$$
\left(6 x^{2}+2 x+3\right)+\left(4 x^{2}-7 x+1\right)
$$
$$
\begin{aligned}
&=\left(6 x^{2}+\quad\right)+(\quad-7 x)+(3+\quad)\\
&=\quad-5 x+
\end{aligned}
$$

Julie S.

Numerade Educator

01:06

Problem 12

Fill in the blanks to add (subtract) the polynomials.
$$
\left(6 x^{2}+2 x+3\right)-\left(4 x^{2}-7 x+1\right)
$$
$$
\begin{aligned}
&=6 x^{2}+2 x+3 \quad 4 x^{2} \quad 7 x-1\\
&=\quad+9 x+
\end{aligned}
$$

Julie S.

Numerade Educator

00:21

Problem 13

Simplify each polynomial and write it in descending powers of one variable.
$$
8 t^{2}+4 t^{2}
$$

Julie S.

Numerade Educator

00:20

Problem 14

Simplify each polynomial and write it in descending powers of one variable.
$$
15 x^{2}+10 x^{2}
$$

Julie S.

Numerade Educator

01:01

Problem 15

Simplify each polynomial and write it in descending powers of one variable.
$$
18 x^{2}-19 x+2 x^{2}
$$

Julie S.

Numerade Educator

01:06

Problem 16

Simplify each polynomial and write it in descending powers of one variable.
$$
17 y^{2}-22 y-y^{2}
$$

Julie S.

Numerade Educator

01:15

Problem 17

Simplify each polynomial and write it in descending powers of one variable.
$$
10 x^{2}-8 x+9 x-9 x^{2}
$$

Julie S.

Numerade Educator

01:24

Problem 18

Simplify each polynomial and write it in descending powers of one variable.
$$
-3 y^{2}-y-6 y^{2}+7 y
$$

Julie S.

Numerade Educator

02:27

Problem 19

Simplify each polynomial and write it in descending powers of one variable.
$$
\frac{1}{5} x^{2}-\frac{3}{8} x+\frac{2}{3} x^{2}+\frac{1}{4} x
$$

Julie S.

Numerade Educator

02:41

Problem 20

Simplify each polynomial and write it in descending powers of one variable.
$$
\frac{6}{7} y^{2}+\frac{1}{2} y-\frac{2}{3} y^{2}+\frac{1}{5} y
$$

Julie S.

Numerade Educator

01:37

Problem 21

Simplify each polynomial and write it in descending powers of one variable.
$$
0.6 x^{3}+0.8 x^{4}+0.7 x^{3}+\left(-0.8 x^{4}\right)
$$

Julie S.

Numerade Educator

01:51

Problem 22

Simplify each polynomial and write it in descending powers of one variable.
$$
1.9 m^{4}-2.4 m^{6}-3.7 m^{4}+2.8 m^{6}
$$

Julie S.

Numerade Educator

00:34

Problem 23

Simplify each polynomial and write it in descending powers of one variable.
$$
\frac{1}{2} s t+\frac{3}{2} s t
$$

Julie S.

Numerade Educator

00:27

Problem 24

Simplify each polynomial and write it in descending powers of one variable.
$$
\frac{2}{5} a t+\frac{1}{5} a t
$$

Julie S.

Numerade Educator

00:30

Problem 25

Simplify each polynomial and write it in descending powers of one variable.
$$
-4 a b+4 a b-a b
$$

Julie S.

Numerade Educator

00:40

Problem 26

Simplify each polynomial and write it in descending powers of one variable.
$$
x y-4 x y-2 x y
$$

Julie S.

Numerade Educator

02:25

Problem 27

Simplify each polynomial and write it in descending powers of one variable.
$$
4 x^{2} y+5-6 x^{3} y-3 x^{2} y+2 x^{3} y
$$

Julie S.

Numerade Educator

02:21

Problem 28

Simplify each polynomial and write it in descending powers of one variable.
$$
5 b-9 a b^{2}+10 a^{3} b-8 a b^{2}-9 a^{3} b
$$

Julie S.

Numerade Educator

01:35

Problem 29

Add the polynomials.
$$
\left(3 q^{2}-5 q+7\right)+\left(2 q^{2}+q-12\right)
$$

Julie S.

Numerade Educator

01:25

Problem 30

Add the polynomials.
$$
\left(2 t^{2}+11 t-15\right)+\left(-5 t^{2}-13 t+10\right)
$$

Julie S.

Numerade Educator

03:14

Problem 31

Add the polynomials.
$$
\left(\frac{2}{3} y^{3}+\frac{3}{4} y^{2}+\frac{1}{2}\right)+\left(\frac{1}{3} y^{3}+\frac{1}{5} y^{2}-\frac{1}{6}\right)
$$

Julie S.

Numerade Educator

02:56

Problem 32

Add the polynomials.
$$
\left(\frac{1}{16} r^{6}+\frac{1}{2} r^{3}-\frac{11}{12}\right)+\left(\frac{9}{16} r^{6}+\frac{9}{4} r^{3}+\frac{1}{12}\right)
$$

Julie S.

Numerade Educator

01:16

Problem 33

Add the polynomials.
$$
(0.3 p+2.1 q)+(0.4 p-3 q)
$$

Julie S.

Numerade Educator

01:24

Problem 34

Add the polynomials.
$$
(-0.3 r-5.2 s)+(0.8 r-5.2 s)
$$

Julie S.

Numerade Educator

01:28

Problem 35

Add the polynomials.
$$
\left(2 x^{2}+x y+3 y^{2}\right)+\left(5 x^{2}-y^{2}\right)
$$

Julie S.

Numerade Educator

01:44

Problem 36

Add the polynomials.
$$
\left(-4 a^{2}-a b+15 b^{2}\right)+\left(5 a^{2}-b^{2}\right)
$$

Julie S.

Numerade Educator

02:37

Problem 37

Find a polynomial that represents the perimeter of the figure.
(angle cant copy)

Julie S.

Numerade Educator

02:23

Problem 38

Find a polynomial that represents the perimeter of the figure.
(angle cant copy)

Julie S.

Numerade Educator

02:29

Problem 39

Find a polynomial that represents the perimeter of the figure.
(angle cant copy)

Julie S.

Numerade Educator

03:10

Problem 40

Find a polynomial that represents the perimeter of the figure.
(angle cant copy)

Julie S.

Numerade Educator

00:51

Problem 41

Use vertical form to add the polynomials.
$$
\begin{array}{l}
{3 x^{2}+4 x+5} \\
{2 x^{2}-3 x+6} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

00:46

Problem 42

Use vertical form to add the polynomials.
$$
\begin{array}{l}
{6 x^{3}-4 x^{2}+7} \\
{7 x^{3}+9 x^{2}+12} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

00:58

Problem 43

Use vertical form to add the polynomials.
$$
\begin{array}{l}
{6 a^{2}+7 a+9} \\
{-9 a^{2}} \quad {-2} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

00:57

Problem 44

Use vertical form to add the polynomials.
$$
\begin{array}{l}
{-2 c^{2}-3 c-5} \\
{14 c^{2}} \quad \quad {-1} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:32

Problem 45

Use vertical form to add the polynomials.
$$
\begin{array}{r}
{z^{3}+6 z^{2}-7 z+16} \\
{9 z^{3}-6 z^{2}+8 z-18} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:13

Problem 46

Use vertical form to add the polynomials.
$$
\begin{array}{l}
{3 x^{3}+4 x^{2}-3 x+5} \\
{3 x^{3}-4 x^{2}-x-7} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:29

Problem 47

Use vertical form to add the polynomials.
$$
\begin{array}{l}
{-3 x^{3} y^{2}+4 x^{2} y-4 x+9} \\
{2 x^{3} y^{2}} \quad \quad \quad \quad {+9 x-3} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

00:53

Problem 48

Use vertical form to add the polynomials.
$$
\begin{array}{l}
{3 x^{2} y^{2}+4 x y+25} \\
{5 x^{2} y^{2}} \quad \quad \quad{-12} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:31

Problem 49

Subtract the polynomials.
$$
\left(3 a^{2}-2 a+4\right)-\left(a^{2}-3 a+7\right)
$$

Julie S.

Numerade Educator

01:10

Problem 50

Subtract the polynomials.
$$
\left(2 b^{2}+3 b-5\right)-\left(2 b^{2}-4 b-9\right)
$$

Julie S.

Numerade Educator

01:19

Problem 51

Subtract the polynomials.
$$
\left(-4 h^{3}+5 h^{2}+15\right)-\left(h^{3}-15\right)
$$

Julie S.

Numerade Educator

01:29

Problem 52

Subtract the polynomials.
$$
\left(-c^{5}+5 c^{4}-12\right)-\left(2 c^{5}-c^{4}\right)
$$

Julie S.

Numerade Educator

02:57

Problem 53

Subtract the polynomials.
$$
\left(\frac{3}{8} s^{8}-\frac{3}{4} s^{7}\right)-\left(\frac{1}{3} s^{8}+\frac{1}{5} s^{7}\right)
$$

Julie S.

Numerade Educator

03:44

Problem 54

Subtract the polynomials.
$$
\left(\frac{5}{6} q^{9}-\frac{4}{5} q^{8}\right)-\left(\frac{1}{4} q^{9}+\frac{3}{8} q^{8}\right)
$$

Julie S.

Numerade Educator

01:33

Problem 55

Subtract the polynomials.
$$
\left(5 a b+2 b^{2}\right)-\left(2+a b+b^{2}\right)
$$

Julie S.

Numerade Educator

01:30

Problem 56

Subtract the polynomials.
$$
\left(m n+8 n^{2}\right)-\left(6-5 m n+n^{2}\right)
$$

Julie S.

Numerade Educator

01:49

Problem 57

Use vertical form to subtract the polynomials.
$$
\text { Subtract } 2 x^{2}-2 x+3 \text { from } 3 x^{2}+4 x+5
$$

Julie S.

Numerade Educator

01:44

Problem 58

Use vertical form to subtract the polynomials.
$$
\text { Subtract } 3 y^{2}-6 y+7 \text { from } 6 y^{2}+4 y+13
$$

Julie S.

Numerade Educator

02:15

Problem 59

Use vertical form to subtract the polynomials.
$$
\text { Subtract }\left(s^{2}+4 s+2\right) \text { from }\left(5 s^{2}+9\right)
$$

Julie S.

Numerade Educator

02:02

Problem 60

Use vertical form to subtract the polynomials.
$$
\text { Subtract }\left(4 p^{2}-4 p-40\right) \text { from }\left(10 p^{2}-30\right)
$$

Julie S.

Numerade Educator

02:19

Problem 61

Use vertical form to subtract the polynomials.
$$
\text { Subtract } 8 a^{3}+8 a^{2}-3 a+1 \text { from } 17 a^{3}+25 a-10
$$

Julie S.

Numerade Educator

02:41

Problem 62

Use vertical form to subtract the polynomials.
$$
\text { Subtract } m^{3}+20 m^{2}-15 m+39 \text { from }-4 m^{3}-m+22
$$

Julie S.

Numerade Educator

01:41

Problem 63

Use vertical form to subtract the polynomials.
$$
\begin{array}{l}
\quad {0.8 x^{3} \quad \quad \quad\quad-2.3 x+0.6} \\
{-\left(0.2 x^{3}-1.2 x^{2}-3.6 x+0.9\right)} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:44

Problem 64

Use vertical form to subtract the polynomials.
$$
\begin{array}{l}
\quad{9.7 y^{3} \quad\quad\quad\quad+\quad y+1.1} \\
{-\left(6.3 y^{3}-4.4 y^{2}+2.7 y+8.8\right)} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

03:08

Problem 65

Subtract $\left(3 x^{2}+4 x-7\right)$ from the sum of $\left(-2 x^{2}-7 x+1\right)$ and $\left(-4 x^{2}+8 x-7\right)$

Julie S.

Numerade Educator

03:20

Problem 66

Subtract $\left(32 x^{2}-17 x+45\right)$ from the sum of $\left(23 x^{2}-12 x-7\right)$ and $\left(-11 x^{2}+12 x+7\right)$

Julie S.

Numerade Educator

02:59

Problem 67

Subtract $t^{3}-2 t^{2}+2$ from the sum of $3 t^{3}+t^{2}$ and $-t^{3}+6 t-3$

Julie S.

Numerade Educator

03:38

Problem 68

Subtract $-3 z^{3}-4 z+7$ from the sum of $2 z^{2}+3 z-7$ and $-4 z^{3}-2 z-3$

Julie S.

Numerade Educator

01:14

Problem 69

Perform the operations.
$$
\left(9 a^{2}+3 a\right)-\left(2 a-4 a^{2}\right)
$$

Julie S.

Numerade Educator

01:06

Problem 70

Perform the operations.
$$
\left(4 b^{2}+3 b\right)-\left(7 b-b^{2}\right)
$$

Julie S.

Numerade Educator

02:05

Problem 71

Perform the operations.
$$
\text { Subtract }\left(-y^{5}+5 y^{4}-1.2\right) \text { from }\left(2 y^{5}-y^{4}\right)
$$

Julie S.

Numerade Educator

02:03

Problem 72

Perform the operations.
$$
\text { Subtract }\left(-4 w^{3}+5 w^{2}+7.6\right) \text { from }\left(w^{3}-15 w^{2}\right)
$$

Julie S.

Numerade Educator

00:49

Problem 73

Perform the operations.
$$
3 r^{4}-4 r+7 r^{4}
$$

Julie S.

Numerade Educator

00:56

Problem 74

Perform the operations.
$$
-2 b^{4}+7 b-3 b^{4}
$$

Julie S.

Numerade Educator

01:48

Problem 75

Perform the operations.
$$
\left(0.03 f^{2}+0.25 f+0.91\right)-\left(0.17 f^{2}-1.18\right)
$$

Julie S.

Numerade Educator

01:54

Problem 76

Perform the operations.
$$
\left(0.05 r^{2}-0.33 r\right)-\left(0.48 r^{2}+0.15 r+2.14\right)
$$

Julie S.

Numerade Educator

03:12

Problem 77

Perform the operations.
$$
\left(\frac{7}{8} r^{4}+\frac{5}{9} r^{2}-\frac{9}{4}\right)-\left(-\frac{3}{8} r^{4}-\frac{2}{3} r^{2}-\frac{1}{4}\right)
$$

Julie S.

Numerade Educator

04:13

Problem 78

Perform the operations.
$$
\left(\frac{4}{5} t^{4}-\frac{1}{3} t^{2}+\frac{1}{2}\right)-\left(-\frac{1}{2} t^{4}+\frac{3}{8} t^{2}-\frac{1}{16}\right)
$$

Julie S.

Numerade Educator

01:24

Problem 79

Perform the operations.
$$
\begin{array}{r}
{8 c^{2}-4 c-5} \\
{-\left(-c^{2}+2 c+9\right)} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:12

Problem 80

Perform the operations.
$$
\begin{array}{l}
{3 t^{3}-4 t^{2}-3 t+5} \\
{+11 t^{3}} \quad\quad {-8 t-2} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:30

Problem 81

Perform the operations.
$$
\left(12.1 h^{3}+9.9 h^{2}\right)+\left(7.3 h^{3}+1.1 h^{2}\right)
$$

Julie S.

Numerade Educator

01:31

Problem 82

Perform the operations.
$$
\left(5.7 n^{3}-2.1 n\right)+\left(-6.2 n^{3}-3.9 n\right)
$$

Julie S.

Numerade Educator

01:38

Problem 83

Perform the operations.
$$
\left(20-4 r t-5 r^{2} t\right)+(10-5 r t)
$$

Julie S.

Numerade Educator

01:30

Problem 84

Perform the operations.
$$
\left(5 m^{2}-8 m+8\right)-\left(-20 m^{2}+m\right)
$$

Julie S.

Numerade Educator

01:47

Problem 85

Perform the operations.
$$
\left(3 x^{2}-3 x-2\right)+\left(3 x^{2}+4 x-3\right)
$$

Julie S.

Numerade Educator

01:35

Problem 86

Perform the operations.
$$
\left(4 c^{2}+3 c-2\right)+\left(3 c^{2}+4 c+2\right)
$$

Julie S.

Numerade Educator

02:31

Problem 87

Perform the operations.
$$
\frac{2}{3} d^{2}-\frac{1}{4} c^{2}+\frac{5}{6} c^{2}-\frac{1}{2} c d+\frac{1}{3} d^{2}
$$

Julie S.

Numerade Educator

02:26

Problem 88

Perform the operations.
$$
\frac{3}{5} s^{2}-\frac{2}{5} t^{2}-\frac{1}{2} s^{2}-\frac{7}{10} s t-\frac{3}{10} s t
$$

Julie S.

Numerade Educator

01:03

Problem 89

Perform the operations.
$$
(3 x+7)+(4 x-3)
$$

Julie S.

Numerade Educator

01:08

Problem 90

Perform the operations.
$$
(2 y-3)+(4 y+7)
$$

Julie S.

Numerade Educator

03:27

Problem 91

Subtract $1.7 t^{2}-1.1 t$ from the sum of $-2.7 t^{2}+2.1 t-1.7$ and $3.1 t^{2}-2.5 t+2.3$

Julie S.

Numerade Educator

03:20

Problem 92

Subtract $1.07 x^{2}-2.07 x$ from the sum of $1.04 x^{2}-5.01$ and $1.33 x-1.9 x^{2}+5.02$

Julie S.

Numerade Educator

00:25

Problem 93

Perform the operations.
$$
-32 u^{3}-16 u^{3}
$$

Julie S.

Numerade Educator

00:24

Problem 94

Perform the operations.
$$
-25 x^{3}-7 x^{3}
$$

Julie S.

Numerade Educator

01:16

Problem 95

Perform the operations.
$$
\left(9 d^{2}+6 d\right)+\left(8 d-4 d^{2}\right)
$$

Julie S.

Numerade Educator

01:30

Problem 96

Perform the operations.
$$
\left(2 c^{2}-4 c\right)+\left(8 c-c^{2}\right)
$$

Julie S.

Numerade Educator

01:50

Problem 97

Perform the operations.
$$
\begin{array}{r}
{3 x^{3} y^{2}+4 x^{2} y+7 x+12} \\
{-\left(-4 x^{3} y^{2}+6 x^{2} y+9 x-3\right)} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

01:41

Problem 98

Perform the operations.
$$
\begin{aligned}
&-2 x^{2} y^{2} \quad \quad \quad \quad+12 y^{2}\\
&-\left(10 x^{2} y^{2}+9 x y-24 y^{2}\right)
\end{aligned}
$$

Julie S.

Numerade Educator

03:11

Problem 99

Perform the operations.
$$
\left(2 x^{2}-3 x+1\right)-\left(4 x^{2}-3 x+2\right)+\left(2 x^{2}+3 x+2\right)
$$

Julie S.

Numerade Educator

03:39

Problem 100

Perform the operations.
$$
\left(-3 z^{2}-4 z+7\right)+\left(2 z^{2}+2 z-1\right)-\left(2 z^{2}-3 z+7\right)
$$

Julie S.

Numerade Educator

00:54

Problem 101

Perform the operations.
$$
\begin{aligned}
&4 x^{3}+4 x^{2}-3 x+10\\
&+\left(5 x^{3}-2 x^{2}-4 x-4\right)
\end{aligned}
$$

Julie S.

Numerade Educator

02:18

Problem 102

Perform the operations.
$$
\begin{array}{r}
{7 m^{5}+m^{3}+9 m^{2}-m} \\
{-\left(8 m^{5}-2 m^{3}+m^{2}+m\right)} \\
\hline
\end{array}
$$

Julie S.

Numerade Educator

02:56

Problem 103

a. $\left(-8 x^{2}-3 x\right)+\left(-11 x^{2}+6 x+10\right)$
b. $\left(-8 x^{2}-3 x\right)-\left(-11 x^{2}+6 x+10\right)$

Julie S.

Numerade Educator

02:51

Problem 104

a. $\left(10-2 s t-3 s^{2} t\right)+(4-6 s t)$
b. $\left(10-2 s t-3 s^{2} t\right)-(4-6 s t)$

Julie S.

Numerade Educator

03:21

Problem 105

Greek Architecture.
a. Find a polynomial that represents the difference in the heights of the columns.
b. If the columns were stacked one atop the other, to what height would they reach?

Julie S.

Numerade Educator

01:32

Problem 106

Jets. Find a polynomial that represents the length of the larger jet.

Julie S.

Numerade Educator

02:06

Problem 107

Pinatas. Find a polynomial that represents the length of the rope used to hold up the piñata.

Julie S.

Numerade Educator

06:02

Problem 108

Reading Blueprints. Find a polynomial that represents
a. the difference in the length and width of the one-bedroom apartment.
b. the perimeter of the apartment.

Julie S.

Numerade Educator

03:50

Problem 109

Naval Operations. Two warning flares are fired upward at the same time from different parts of a ship. The height of the first flare is $\left(-16 t^{2}+128 t+20\right)$ feet and the height of the higher-traveling second flare is $\left(-16 t^{2}+150 t+40\right)$ feet, after $t$ seconds.
a. Find a polynomial that represents the difference in the heights of the flares.
b. In 4 seconds, the first flare reaches its peak, explodes, and lights up the sky. How much higher is the second flare at that time?

Julie S.

Numerade Educator

03:17

Problem 110

Auto Mechanics. The length of a fan belt that wraps around three pulleys is $\left(3 x^{2}+11 x+4.5 \pi\right)$ in. Find a polynomial that represents the unknown length of a part of the belt shown in the illustration below.

Julie S.

Numerade Educator

00:57

Problem 111

How do you recognize like terms?

Julie S.

Numerade Educator

01:29

Problem 112

Explain why the vertical form used in algebra to add $2 x^{2}+4 x+3$ and $5 x^{2}+3 x+6$ is similar to the vertical form used in arithmetic to add 243 and 536

Julie S.

Numerade Educator

01:07

Problem 113

Explain the error below.
$$
7 x^{2} y+6 x^{2} y=13 x^{4} y^{2}
$$

Julie S.

Numerade Educator

01:10

Problem 114

Explain the error below.
$$
\begin{aligned}
\left(12 x^{2}-4\right)-\left(3 x^{2}-1\right) &=12 x^{2}-4-3 x^{2}-1 \\
&=9 x^{2}-5
\end{aligned}
$$

Julie S.

Numerade Educator

01:56

Problem 115

A student was asked to simplify $\frac{1}{6} x^{2}-3+\frac{2}{3} x^{2}$. Explain the error below:
$$
6\left(\frac{1}{6} x^{2}-3+\frac{2}{3} x^{2}\right)=x^{2}-18+4 x^{2}
$$
$5 x^{2}$

Julie S.

Numerade Educator

00:51

Problem 116

Explain the error below.
Subtract $\left(2 d^{2}-d-3\right)$ from $\left(d^{2}-9\right):$
$$
\left(2 d^{2}-d-3\right)=\left(d^{2}-9\right)=d^{2}-d+6
$$

Julie S.

Numerade Educator

00:11