Question

[Mel bel]

Rút gọn biểu thức 

a) (x+y)²+(x-y)²

b) (x-y)²-(x+y)²

c) 2(x-y)(x+y)+(x+y)²+(x-y)²

d) (x+y)²-4xy-(x-y)²

e) (x-2y)(x+2y)+(x+2y)²

Answer 1

[HT.Phong (9A5)]

\(a.\left(x+y\right)^2+\left(x-y\right)^2\\ =x^2+2xy+y^2+x^2-2xy+y^2\\ =2x^2+2y^2\\ b.\left(x-y\right)^2-\left(x+y\right)^2\\ =x^2-2xy+y^2-x^2-2xy-y^2\\ =-4xy\\ c.2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\\ =2\left(x^2-y^2\right)+\left(x^2+2xy+y^2\right)+\left(x^2-2xy+y^2\right)\\ =2x^2-2y^2+x^2+2xy+y^2+x^2-2xy+y^2\\ =4x^2\\ d.\left(x+y\right)^2-4xy-\left(x-y\right)^2\\ =x^2+2xy+y^2-4xy-x^2+2xy-y^2\\ =0\\ e.\left(x-2y\right)\left(x+2y\right)+\left(x+2y\right)^2\\ =x^2-4y^2+x^2+4xy+4y^2\\ =2x^2+4xy\)