Question

Chứng minh các đẳng thức sau:

a) (x-1)(x+1)=x²-1; (x-y)(x+y)=x²-y²; (x-y)²=x²-2xy+y²

b) (x+y)²=x²+2xy+y²; x³-1=(x-1)(x²+x+1); x³-y³=(x-y)(x²+xy+y²)

c) x³+1=(x+1)(x²-x+1); x³+y³=(x+y)(x²-xy+y²)

Answer 1

Nhân phân phối là ra thôi

a)

\(VT=\left(x-1\right)\left(x+1\right)=x.x+x.1-1.x+\left(-1\right).1\)

\(=\left(x^2-1\right)+\left(x-x\right)=x^2-1+0=x^2-1=VP\Rightarrow dccm\)

c) thay vì c/m A=B ta chứng Minh B=A

\(VP=\left(x+1\right)\left(x^2-x+1\right)=\left(x^3-x^2+x\right)+\left(x^2-x+1\right)\)

\(=\left(x^3+1\right)+\left(-x^2+x^2\right)+\left(x-x\right)=x^3+1+0+0=x^3+1=VT\Rightarrow VT=VP\Rightarrow dpcm\)\(=x^3+1+0+0=x^3+1=VT\Rightarrow VT=VP\Rightarrow dpcm\)