Problem

Perform the operations. $$ \begin{array}{r} {8 c^…

01:24

Problem 78 Hard Difficulty

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

Answer

$\frac{13}{10} t^{4}-\frac{17}{24} t^{2}+\frac{9}{26}$

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Algebra

Elementary and Intermediate Algebra 5th

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

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Video Transcript

we're being asked to perform the given operation, and in this particular case, we're being asked to subtract Paulino meals. And the reason why we know this is because in between both sets of Sprem theses, there's a minus sign. Well, how do we subtract Paulina meals? Well, what we're going to do for the first polynomial is we're going to bring down each of the terms as it's so we're gonna have 4/5 t to the fourth minus 1/3 t squared, plus 1/2 now for the second polynomial, the one that means attracted by the first. We're going to go ahead and switch the signs of each of the terms, and then we can drop the parentheses. So, in other words, that negative 1/2 T to the four will become a positive one. Half a t to the fourth. The positive 3/8 t squared will become negative 3/8 T Square, and the negative one over 16 will become positive one over 60. Now, what we wanted Thio using the community and associated properties is we want to combine our like terms together. So let's look at our first term 4 50 to the fourth. Well, it's like term is 1/2 t to the fourth, so we can start with the quantity of 4/5 t to the fourth plus 1/2 t to the fourth, while our next term is negative. 1 30 square. And it's like term is negative. 3/8 t squared so we can group those together. So we'll have, plus the quantity of negative 1/3 T squared minus three x t Square. And now our constant terms. We have positive 1/2 and positive, one over 16. So those will also be like terms. So we'll have, plus the quantity of 1/2 plus won over 16. So now we simply need to combine like terms. So let's start with the first set of parentheses. We have 4 50 to the fourth plus 1/2 T to the fourth, so that means we need to add 4 50 plus 1/2. Well, when adding fractions, we need a common denominator. So in this case, are common denominator is going to be 10. So I need to multiply my first fraction by two over too. My second fraction by five over five. So what will be left with is eight over 10 t to the fourth plus five Overton T to the fourth and our second set of parentheses. We have negative 1/3 T squared minus 3/8 t squared. Well again. When we subtract fractions, we need a common denominator, which in this case, is going to be 24. So I'm going to multiply my first fraction by eight over a my second fraction by three over three. So we'll be left with negative E over 24 T Square minus nine over 24 t squared. And now we'll take a look. The last prophecy. Well, for being asked to add fractions, But again, we're going to need a common denominator, which in this case is 16. So I simply need to multiply my first fraction by eight over eight. The second fraction does not need to change because it's denominator is already 16 so we'll be left with E over 16 plus one over 16. And now we can go ahead and combine our light terms while in our first set of prophecies, we have eight temps t to the fourth plus five times T to the fourth well, 8/10 post five times is 13 thumbs, so we'll have 13 over 10 t to the fourth. In our second set of prophecies, we have negative eight over 24 T squared, minus nine over 24 t squared. Well, negative eight over 24. Minus nine over 24 is negative. 17 over 24. So I'm negative 17 over 24 T Square. And in our last set of prophecies, we have eight over 16 plus one over 16 which is nine over 16. So a plus nine over 16 and this try no meal will be your final answer.

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