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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. 208 (page 604)

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.
$鈭� 2 x^{3} y^{2} - 16 y^{5}$

Short Answer

Expert verified

The factored form of the given expression is $2 y^{2} (x + 2 y) (x^{2} - 2 x y + 4 y^{2})$ .

Step by step solution

01

Step 1. Given information.

The given expression is:
$鈭� 2 x^{3} y^{2} - 16 y^{5}$

02

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl} 鈭� 2 x^{3} y^{2} - 16 y^{5} & = & 鈭� 2 y^{2} (x^{3} + 8 y^{3}) \\ = & 鈭� 2 y^{2} (x^{3} + {(2 y)}^{3}) \\ = & 鈭� 2 y^{2} (x + 2 y) (x^{2} - (x) (2 y) + {(2 y)}^{2}) [鈭� a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})] \\ = & 鈭� 2 y^{2} (x + 2 y) (x^{2} - 2 x y + 4 y^{2}) \end{array}$

03

Step 3. Conclusion.

The factored form of the given expression is $2 y^{2} (x + 2 y) (x^{2} - 2 x y + 4 y^{2})$ .

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