College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.3 - Polynomials - R.3 Exercises - Page 30: 75

Answer

$q^{4} - 8q^{3} + 24q^{2} - 32q + 16$

Work Step by Step

1. Rewrite as product of binomials: $(q - 2)^4$ = $(q-2)^2 \cdot (q-2)^2$ 2. Squaring each we get : $(q-2)^2 \cdot (q-2)^2 = (q^2 - 4q + 4) \cdot (q^2 - 4q + 4)$ 3. Multiply these polynomials: $(q^2 - 4q + 4) \cdot (q^2 - 4q + 4) = q^4 - 4q^3 + 4q^2 - 4q^3 +16q^2 - 16q + 4q^2 - 16q +16$ 4. Combine like terms via addition/subtraction: $q^4 - 4q^3 + 4q^2 - 4q^3 +16q^2 - 16q + 4q^2 - 16q +16 = q^{4} - 8q^{3} + 24q^{2} - 32q + 16$ The result is $q^{4} - 8q^{3} + 24q^{2} - 32q + 16$
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