Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 8 - Polynomials and Factoring - 8-7 Factoring Special Cases - Practice and Problem-Solving Exercises - Page 516: 58



Work Step by Step

We use the formula for the difference of squares to apply to this question. The difference of squares formula is: $(a-b) (a+b) = a^{2} - b^{2}$ = 4($64g^{4}$ - $25h^{6}$) *** Take the square root of $64g^{4}$ which is $8g^{2}$. Becuase $8g^{2}$ × $8g^{2}$ = $64g^{4}$ *** Take the square root of $25h^{6}$ which is $5h^{3}$. Becuase $5h^{3}$ × $5h^{3}$ = $25h^{6}$ = 4($(8g^{2})^{2}−(5h^{3})^{2}$) In the given formula let $8g^{2}$ represents a and $5h^{3}$ represents b. 4($(8g^{2})^{2}−(5h^{3})^{2}$) = 4$(8g^{2}+5h^{3})(8g^{2}-5h^{3})$
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