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: 109

Answer

The statement $(x+1)^2=x^2+1$ is false. The correct statement is $(x+1)^2=x^2+2x+1$.

Work Step by Step

The square of a binomial can be found using the formula $(a+b)^2=a^2+2ab+b^2$. The square of the sum of two terms is NOT the sum of the square of each term.. $$(x+1)^2=x^2+2(x)(1)+1^2$$ $$=x^2+2x+1$$ The statement$(x+1)^2=x^2+1$ is false because the second term is missing. The correct statement is $(x+1)^2=x^2+2x+1$.
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