Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Review - Exercises: 29

Answer

$4(2-t)(2+t)$ or $-4(t-2)(t+2)$

Work Step by Step

$16-4t^{2}$ This a difference of squares. The formula for factoring an expression like this is $A^{2}-B^{2}=(A-B)(A+B)$. For this expression, $A=16$ and $B=4t^{2}$. Apply the formula to factor the expression: $16-4t^{2}=(4-2t)(4+2t)=...$ Take common factor $2$ from both parentheses and simplify: $...=(2)(2-t)(2)(2+t)=4(2-t)(2+t)$
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