Question

Chứng Minh:

a) (x²+y²)²-(2xy)²=(x+y)²(x-y)²

Answer 1

Ta có: \(VT=\left(x^2+y^2\right)^2-\left(2xy\right)^2\)

\(=\left(x^2+2xy+y^2\right)\left(x^2-2xy+y^2\right)\)

\(=\left(x-y\right)^2\left(x+y\right)^2=VP\)

\(\Rightarrowđpcm\)

Answer 2

\(\left(x^2+y^2\right)^2-\left(2xy\right)^2=\left(x^2+y^2-2xy\right)\left(x^2+y^2+2xy\right)=\left(x-y\right)^2\left(x+y\right)^2\)