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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 350 (page 634)

In the following exercises, factor by grouping.
$x^{2} y - x y^{2} + 2 x - 2 y$

Short Answer

Expert verified

The factored form of the polynomial is,

$(x - y) (x y + 2)$

Step by step solution

01

Step 1. Given Information

We are given a polynomial,

$x^{2} y - x y^{2} + 2 x - 2 y$

02

Step 2. Factorizing the polynomial

Grouping the terms, we get

$x^{2} y - x y^{2} + 2 x - 2 y = (x^{2} y - x y^{2}) + (2 x - 2 y)$

Factoring out GCF, we get

$x^{2} y - x y^{2} + 2 x - 2 y = x y (x - y) + 2 (x - y)$

Again factoring out GCF, we get

$x^{2} y - x y^{2} + 2 x - 2 y = (x - y) (x y + 2)$

03

Step 3. Checking the factorization

Multiplying the factors,

$(x - y) (x y + 2) = x^{2} y - x y^{2} + 2 x - 2 y x (x y + 2) - y (x y + 2) = x^{2} y - x y^{2} + 2 x - 2 y x^{2} y - x y^{2} + 2 x - 2 y = x^{2} y - x y^{2} + 2 x - 2 y L H S = R H S$

Hence the factorization is correct.

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