Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Review - Concept Check - Page 132: 11

Answer

$$ a^{2}+2ab+b^{2}$$ $$ a^{2}-2ab+b^{2}$$ $$ a^{3}+3a^{2}b+3ab^{2}+b^{3}$$ $$ a^{3}-3a^{2}+3ab^{2}-b^{3}$$ $$ a^{2}-b^{2}$$ $$ x^{2}+10x+25$$ $$ x^{2}-25$$

Work Step by Step

(i) $$(a+b)^{2}$$ $$(a+b)(a+b)$$ $$a^{2}+ab+ab+b^{2}$$ $$Answer: a^{2}+2ab+b^{2}$$ (ii) $$(a-b)^{2}$$ $$(a-b)(a-b)$$ $$a^{2}-ab-ab+b^{2}$$ $$Answer: a^{2}-2ab+b^{2}$$ (iii) $$(a+b)^{3}$$ $$Answer: a^{3}+3a^{2}b+3ab^{2}+b^{3}$$ (iv) $$(a-b)^{3}$$ $$Answer: a^{3}-3a^{2}+3ab^{2}-b^{3}$$ (v) $$(a+b)(a-b)$$ $$Answer: a^{2}-b^{2}$$ EXPAND $$(x+5)^{2}$$ $$Answer: x^{2}+10x+25$$ $$(x+5)(x-5)$$ $$Answer: x^{2}-25$$
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