Question

Rút gọn

a) M= (x + y + z)² + (y + z)² - 2(y + z) . (x + y +z)

b) N= (x - 1)³ + (x + 1)³

Answer 1

\(M=\left(x+y+z\right)^2+\left(y+z\right)^2-2\left(y+z\right)\left(x+y+z\right)=\left[\left(x+y+z\right)-\left(y+z\right)\right]^2=x^2\)\(N=\left(x-1\right)^3+\left(x+1\right)^3=\left[\left(x-1\right)+\left(x+1\right)\right]\left[\left(x-1\right)^2-\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\right]\)=\(2x\left(x^2-2x+1-x^2+1+x^2+2x+1\right)=2x\left(2x+3\right)\)

Answer 2

a, \(M=\left(x+y+z\right)^2+\left(y+z\right)^2-2\left(y+z\right)\left(x+y+z\right)\)

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

\(=x^2+2y^2+2z^2+2xy+4yz+2xz-2xy-2y^2-2yz-2xz-2yz-2z^2\)

\(=x^2\)

b, \(N=\left(x-1\right)^3+\left(x+1\right)^3\)

\(=x^3-3x^2+3x-1+x^3+3x^2+3x+1\)

\(=2x^3+6x\)

Answer 3

Ta có :

a, M =\(\left(x+y+z\right)^2+\left(y+z\right)^2-2\left(y+z\right)\left(x+y+z\right)\)

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

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

\(=x^2\)

b,\(N=\left(x-1\right)^3+\left(x+1\right)^3\)

\(=\left(x-1+x+1\right)\left(\left(x-1\right)^2-\left(x-1\right)\left(x+1\right)-\left(x+1\right)^2\right)\)

\(=2x\left(x^2-2x+1-x^2+x-x+1+x^2+2x+1\right)\)

=\(2x\left(x^2+3\right)=2x^3+6x\)