# Chapter 8 - Polynomials and Factoring - 8-7 Factoring Special Cases - Practice and Problem-Solving Exercises - Page 527: 43

$33x^{2}-80x+7$

#### Work Step by Step

a)Subtract by combining like terms $(49x^{2}-56x+16)-(16x^{2}+24x+9)$ ..remove parentheses. $=49x^{2}-56x+16-16x^{2}-24x-9$ ...combine like terms. $=(49x^{2}-16x^{2})+(-56x-24x)+(16-9)$ $=33x^{2}-80x+7$ or b) Factor each expression and then use the rule for a difference of two squares. $(49x^{2}-56x+16)-(16x^{2}+24x+9)$ ...write each expression as a square of a binomial. $=(7x-4)^{2}-(4x+3)^{2}$ ...use the rule for a difference of two squares. $=[(7x-4)+(4x+3)][(7x-4)-(4x+3)]$ ...remove the inner parentheses and combine like terms. $=(7x-4+4x+3)(7x-4-4x-3)$ $=(11x-1)(3x-7)$ ...multiply the parentheses. $=33x^{2}-77x-3x+7$ ...add like terms. $=33x^{2}-80x+7$

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