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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q 52E (page 1069)

In the following exercises, factor.
$鈭� 4 x^{3} y^{5} 鈭� x^{2} y^{3} + 12 x y^{4}$ .

Short Answer

Expert verified

The obtained factor for the expression $鈭� 4 x^{3} y^{5} 鈭� x^{2} y^{3} + 12 x y^{4}$ is, $- x y^{3} (4 x^{2} y^{2} + x - 12 y)$ .

Step by step solution

01

Given expression is,

$鈭� 4 x^{3} y^{5} 鈭� x^{2} y^{3} + 12 x y^{4}$ .

The objective is, we need to find the factor for this expression.

02

Step 2 First find the GCF for the given expression.

$鈭� 4 x^{3} y^{5} = - 2 脳 2 脳 x 脳 x 脳 x 脳 y 脳 y 脳 y 脳 y 脳 y 鈭� x^{2} y^{3} = - 1 脳 x 脳 x 脳 y 脳 y 脳 y 12 x y^{4} = 2 脳 6 脳 x 脳 y 脳 y 脳 y 脳 y$

The GCF is, $x y^{3}$ .

03

In the given expression, rewrite the each term using GCF.

$鈭� 4 x^{3} y^{5} 鈭� x^{2} y^{3} + 12 x y^{4} = x y^{3} (- 4 x^{2} y^{2}) + x y^{3} (- x) + x y^{3} (12 y)$

Now factor out the GCF.

$鈭� 4 x^{3} y^{5} 鈭� x^{2} y^{3} + 12 x y^{4} = x y^{3} (- 4 x^{2} y^{2} - x + 12 y) = - x y^{3} (4 x^{2} y^{2} + x - 12 y)$

The obtained factor is, $- x y^{3} (4 x^{2} y^{2} + x - 12 y)$

04

Step 4 Let us check the answer by multiplying the factors.

$- x y^{3} (4 x^{2} y^{2} + x - 12 y) = 鈭� 4 x^{3} y^{5} 鈭� x^{2} y^{3} + 12 x y^{4}$

which is true.

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