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

$$\frac{7}{12} c^{2}-\frac{1}{2} c d+d^{2}$$

Algebra

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

Polynomials

Campbell University

McMaster University

University of Michigan - Ann Arbor

Lectures

01:14

Perform the indicated oper…

01:35

Perform the operations.

01:47

01:48

01:51

00:43

00:51

01:41

Perform the given operatio…

03:14

00:45

01:24

00:39

Perform the operations. Th…

01:30

00:55

02:18

01:59

02:40

Multiply.$$\left(3…

00:36

Perform the operations and…

01:08

this problem. We're being asked to perform to given operations and for this particular example. Essentially, we're being asked to simplify this polynomial, meaning we want to combine our life terms while using the community of an associative properties. We can re group and reorder our terms so that way are glowing. Terms are together. So let's start with the first term. 2/3 D squared. Well, it's like term is plus 1/3 D squared so we can group these together so we'll have the quantity of 2/3 D squared plus 1/3 D squared. Now let's move to the next term, which is negative. 1/4 C square. Well, it's like term is positive. 56 c squared. So we'll group these together so we'll have, plus the quantity of negative 1/4 C square plus five over six C Square. And now our last term is negative. 1/2 CD. Well, it does not have a life term, but we simply need to bring it down for our final answer. So now we can go ahead and try and combine our life terms. So let's look at our first set of Prem theses. Well, we have 2/3 D squared plus 1/3 D squared well, 2/3 plus 1/3 is 3/3. So we'll have 3/3 D square. Now, let's look at our second set of prophecies. Well, we have negative 1/4 C squared plus five six C squared. Well, we're being asked to add these two fractions, but we're gonna need a common denominator, which in this case, is 12. So for my first fraction, I'm gonna multiply the numerator and the denominator by three. And for the second fraction, multiply the numerator and denominator by two. So we will be left with, plus the quantity of negative 3 12 c squared, pause, 10 twelves, C square. And again, we're still just going to bring down our last term there of 1/2 negative 1/2 C square. Well, let's look at that First term we have three over three D squared. Well, three over three is equal, the one so we're just left with D Square. Now let's combine those like terms in our friend Vusi. Well, negative three twelves plus 10 twelves is seven twelves, so we will be left with 7/12 C square and again we're just gonna bring down our last. Her minus 1/2 CD and D squared plus 7 12 c squared minus 1/2 CD is our final answer.

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03:11

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01:05

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01:22

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00:41

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00:47

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