College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.4: 107

Answer

The statement $(3x^3+2)(3x^3-2)=9x^9-4$ is false. The correct statement is $(3x^3+2)(3x^3-2)=9x^6-4$.

Work Step by Step

The product of the sum and difference of two terms can be found using the formula $(a+b)(a-b)=a^2-b^2$. $$(3x^3+2)(3x^3-2)=(3x^3)^2-2^2$$ To raise an exponent to an exponent, multiply the exponents: $$=9x^{(3\times 2)}-4$$ $$=9x^6-4$$
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