Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 5 - Section 5.1 - Adding and Subtracting Polynomials - Exercise Set - Page 351: 111

Answer

Explanation given below.

Work Step by Step

A polynomial is an expression containing one term, or the sum of several terms which have the form term =(real number)$\times$(power of a variable)$\times$(power of a variable)$\times$...$\times$(power of a variable) The terms can contain one or more variables. To $\text{subtract two polynomials,}$ first, distribute the minus in front of the second polynomial, that is, change all the signs of the terms of the second polynomial, and then add the polynomials. (To add polynomials, group like terms and add them. Like terms are terms with exactly the same variable parts.) Example: $(7x^{3}-2xy^{2}+3y^{2}-x)-(-x^{3}+y^{2}-xy^{2}-4)$ $=(7x^{3}-2xy^{2}+3y^{2}-x)+(x^{3}-y^{2}+xy^{2}+4)$ Terms with $x^{3}:\qquad 7x^{3}+x^{3}=8x^{3}$ Terms with $xy^{2}:\qquad -2xy^{2}+xy^{2}=-xy^{2}$ Terms with $y^{2}:\qquad 3y^{2}-y^{2}=2y^{2}$ Terms with $x:\qquad-x$ Constant terms$:\qquad 4$ difference = $8x^{3}-xy^{2}+2y^{2}-x-4$
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