Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises: 76

Answer

(a + b + 3)(2a + 2b - 1)

Work Step by Step

First, it is easiest to pretend the a + b term is just an x, then substitute a + b back into the equation at the end. Because the first term has a coefficient other than 1, you must first multiply the first coefficient by the last one, and try to find two factors of this product that sum to the coefficient of the second term. In this case, multiply 2 by -3 for -6, and find two factors, 6 and -1, that add to the middle coefficient, 5. The expression is then rewritten, and instead of the original middle term, the two factors found are now inserted into the expression, giving: 2$x^2$ + 6x - x - 3 Now the first two terms are grouped together and the last two terms are grouped together, and each is factored as a binomial. giving: 2x(x + 3) - 1(x + 3) (x + 3)(2x - 1) Now substitute a + b back into the equation (a + b + 3)(2a + 2b - 1)
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