# Chapter 8 - Polynomials and Factoring - Pull it All Together - Page 522: Task 1

$7y^2*\pi + 2xy*\pi$

#### Work Step by Step

bulls eye has radius $x$ 4 outer rings each have radius $y$ area of outermost ring desired area of outer ring = area of circle - area of inner three rings $A = \pi*r^2 - \pi*r^2$ $A = \pi * (x+4y)^2 - \pi*(x+3y)^2$ $A = \pi * (x+4y)(x+4y) - \pi * (x+3y)(x+3y)$ $A = \pi * (x^2+4xy+4xy+16y^2) - \pi * (x^2+3xy+3xy+9y^2)$ $A = \pi * (x^2+8xy+16y^2) - \pi * (x^2+6xy+9y^2)$ $A = \pi * (x^2+8xy+16y^2-x^2-6xy-9y^2)$ $A = \pi * (8xy+16y^2-6xy-9y^2)$ $A = \pi * (2xy+7y^2)$ $A = \pi * (7y^2 + 2xy)$ $A = 7y^2*\pi + 2xy*\pi$

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