Algebra 1

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

Chapter 8 - Polynomials and Factoring - 8-8 Factoring by Grouping - Practice and Problem-Solving Exercises: 45

Answer

$(2^{5} + 2^{4} + 2^{3}) + (2^{2} + 2^{1} + 2^{0})$ = (9)(7) = 63

Work Step by Step

$(2^{5} + 2^{4} + 2^{3}) + (2^{2} + 2^{1} + 2^{0})$ We factor the GCF from the first three terms and the last three terms $2^{3}(2^{2} + 2^{1} + 2^{0}) + 1(2^{2} + 2^{1} + 2^{0})$ We factor out the common $(2^{2} + 2^{1} + 2^{0})$ and we get $(2^{3} + 1)(2^{2} + 2^{1} + 2^{0})$ We simplify the brackets $2^{3}$ = 2*2*2 = 8 $2^{2}$ = 2*2 = 4 $2^{1}$ = 2 $2^{0}$ = 1 (8+1) (4+2+1) (9)(7) 63
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