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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 273 (page 538)

In the following exercises , simplify the equation $(2 x^{2} 鈥� 鈭� 鈥� 3 y^{4}) (2 x^{2} 鈥� + 鈥� 3 y^{4})$ .

Short Answer

Expert verified

The simplified expression is $4 x^{4} - 9 y^{8}$ .

Step by step solution

01

Step 1. Given Information.

The expression is $(2 x^{2} 鈥� 鈭� 鈥� 3 y^{4}) (2 x^{2} 鈥� + 鈥� 3 y^{4})$ .

02

Step 2. Simplify given equation.

Simplifying $(2 x^{2} 鈥� 鈭� 鈥� 3 y^{4}) (2 x^{2} 鈥� + 鈥� 3 y^{4})$

Apply Difference of two squares formula:-

$(a - b) (a + b) = a^{2} - b^{2} (2 x^{2} - 3 y^{4}) (2 x^{2} + 3 y^{4}) = {(2 x^{2})}^{2} - {(3 y^{4})}^{2} {(2 x^{2})}^{2} - {(3 y^{4})}^{2} = 4 x^{4} - 9 y^{8}$

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