Answer
$7y^2*\pi + 2xy*\pi$
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
$A = \pi*r^2 - \pi*r^2$
$A = \pi * (x+4y)^2 - \pi*(x+3y)^2$
$A = \pi * (x+4y)(x+4y) - \pi * (x+3y)(x+3y)$
$A = \pi * (x^2+4xy+4xy+16y^2) - \pi * (x^2+3xy+3xy+9y^2)$
$A = \pi * (x^2+8xy+16y^2) - \pi * (x^2+6xy+9y^2)$
$A = \pi * (x^2+8xy+16y^2-x^2-6xy-9y^2)$
$A = \pi * (8xy+16y^2-6xy-9y^2)$
$A = \pi * (2xy+7y^2)$
$A = \pi * (7y^2 + 2xy)$
$A = 7y^2*\pi + 2xy*\pi$
