Đáp án:
Giải thích các bước giải:
a, `(x + y)^2 + (x – y)^2`
`= x^2+2xy+y^2+x^2-2xy+y^2`
`=2x^2+2y^2`
b) `2(x – y)(x + y) + (x + y)^2 + (x – y)^2`
`=2(x^2-y^2)+x^2+2xy+y^2+x^2-2xy+y^2`
`=2x^2-2y^2+x^2+2xy+y^2+x^2-2xy+y^2`
`=4x^2`
c) `(x – y + z)^2 + (z – y)^2 + 2(x – y + z)(y – z)`
\(=\left(x-y+z\right)^2+\left(z-y\right)^2+\left(x-y+z\right)\left(y-z\right)+\left(x-y+z\right)\left(y-z\right)\)
\(=\left(x-y+z\right)^2+\left(x-y+z\right)\left(y-z\right)+\left(z-y\right)^2+\left(x-y+z\right)\left(y-z\right)\)
\(=\left(x-y+z\right)^2+\left(x-y+z\right)\left(y-z\right)+\left(z-y\right)^2-\left(x-y+z\right)\left(z-y\right)\)
\(=\left(x-y+z\right)\left(x-y+y+z-z\right)+\left(z-y\right)[z-y-\left(x-y+z\right)]\)
\(=\left(x-y+z\right)x+\left(z-y\right)\left(z-y-x+y-z\right)\)
\(=x^2-xy+xz+\left(z-y\right)\left(-x\right)\)
\(=x^2-xy+xz-xz+xy\)
\(=x^2\)
