Question

化简[(x^2+y^2)^2-4x^2y^2]÷（x+y)^2,其中x=1,y=3/2

Answer 1

[(x^2+y^2)^2-4x^2y^2]÷（x+y)^2

=[(x^2+y^2)^2-(2xy)^2]÷（x+y)^2

=[(x^2+y^2+2xy)(x^2+y^2-2xy)]÷（x+y)^2,[a²-b²=(a+b)(a-b)]

=[(x+y)^2(x-y)^2]÷（x+y)^2

=(x-y)^2

=(1-3/2)²

=(-1/2)²

=1/4