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

$$7 x^{3} y^{2}-2 x^{2} y-2 x+15$$

Algebra

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

Polynomials

Missouri State University

Oregon State University

Idaho State University

Lectures

01:23

Perform the operations.

00:41

Perform indicated operatio…

01:42

01:32

Perform the indicated oper…

01:26

02:00

04:38

01:54

01:08

Perform the operations and…

04:04

Perform each indicated ope…

01:11

01:38

02:17

we're being asked to perform to given operations, while in this particular case we're being asked to subtract two palling, no meals. You'll also notice that they wrote this problem in vertical form. Well, just distract you, Paulie. No meals. We simply need to change the sign off each of the terms in appalling no meal getting subtracted from the original polynomial, which is which in this case is the second row. So what we're going to do is we're going to rewrite our first row. As so we're gonna have three x to the third y squared plus four x squared Y plus seven x plus 12. Now for a second row, we need to change each of the signs. So the negative four x to the third y squared will become positive for X to the third. Why square the positive six x squared y will become negative six. X squared y the positive nine next will become negative. Nynex and the negative three will become positive three. And now we're all set to combine our late terms. And if you know this, all of our like terms are written and columns. We'll start with the first column we have three x to the third y squared plus four x 1/3 y squared. Well, three plus four is seven. So we'll have seven x to the third. Why square in our second calm? We have four x squared y minus six x squared y Well, four minus six is negative too. So we'll have negative too X squared y. Now, In our third call, we have seven x minus Nynex. Well, seven minus nine is negative, too, so we'll have negative to X. And in our last column, we have 12 Blustery, which is positive. 15. So our final answer is seven x to the third y squared minus two X squared y minus two x plus 15.

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