Question

Chứng minh rằng:

(x+y+z)²=x²+y²+z²+2xy+2yz+2zx

(x+y+z)³=x³+y³+z³+3(x+y)(y+z)(z+x)

Giúp e bài này với ạ

Answer 1

a: \(VT=\left(x+y\right)^2+2z\left(x+y\right)+z^2\)

\(=x^2+y^2+z^2+2xy+2xz+2yz\)

b: \(VT=\left(x+y\right)^3+3\left(x+y\right)^2\cdot z+3\left(x+y\right)\cdot z^2+z^3\)

\(=x^3+y^3+z^3+3\left(x+y\right)\left(y+z\right)\left(x+z\right)\)

Answer 2

`(x+y+z)^2 = x^2 + xy + xz + xy + y^2 + yz + xz + yz + z^2`

`= x^2 + y^2 + z^2 + 2xy + 2yz + 2xz`

`(x+y+z)^3 = (x^2+y^2+z^2+2xy+2yz+2xz)(x+y+z)`

`= x^3 + y^3 + z^3 + 3(x+y)(y+z)(z+x)`.