Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 1 - Section 1.4 - Basic Rules of Algebra - Exercise Set - Page 55: 95

Answer

False. In general, $a+(bc)\neq(a+b)(a+c)$; in words, addition can not be distributed over multiplication.

Work Step by Step

For the equality to be true, it must be true for all a,b,c. Counterexample: a=1, b=2, c=0 LHS = $1+(2\cdot 0)=1$ RHS = $(1+2)(1+0)=3(1)=3$ so, the statement is false. To make it true, replace $=$ with $\neq$. False. In general, $a+(bc)\neq(a+b)(a+c)$; in words, addition can not be distributed over multiplication.
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