Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 7 - Polynomial Equations and Factoring - 7.3 - Special Products of Polynomials - Exercises - Page 376: 46

Answer

$(x+1)^{3}=x^{3}+3x^{2}+3x+1$ $(x+2)^{3}=x^{3}+6x^{2}+12x+8$ $(a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$

Work Step by Step

$(x+1)^{3}=(x+1)^{2}(x+1)$ $=(x^{2}+2x+1)(x+1)$ $=x^{3}+x^{2}+2x^{2}+2x+x+1$ $=x^{3}+3x^{2}+3x+1$ $(x+2)^{3}=(x+2)^{2}(x+2)$ $=[x^{2}+2(x)(2)+2^{2}](x+2)$ $=(x^{2}+4x+4)(x+2)$ $=x^{3}+2x^{2}+4x^{2}+8x+4x+8$ $=x^{3}+6x^{2}+12x+8$ We infer from the above two expansions that $(a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$
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