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: 108


The statement $(x-5)^2=x^2-5x+25$ is false. The correct statement is $(x-5)^2=x^2-10x+25$.

Work Step by Step

The square of a binomial can be found using the formula $(a-b)^2=a^2-2ab+b^2$. $$(x-5)^2=x^2-2(x)(5)+5^2$$ $$=x^2-10x+25$$ The statement $(x-5)^2=x^2-5x+25$ is false because the second term is incorrect. The correct statement is $(x-5)^2=x^2-10x+25$.
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