A family is having a pool built in their backyard. If their yard is rectangular and measures 10x by 10x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built? Write your answer in factored form.

Area of rectangle=legnth times width

area of circle=pi time radius^2

are left=yard-pool

given

legnth an dwidth are 10x

area=10x times 10x=100x^2=yard

area of pool=

pi times (2x) ^2

pi times 4x^2

4pix^2=pool

yard-pool=100x^2-4pix^2 = (100-4pi) x^2

aprox

87.42x^2 of the yard

minus