Question

Chứng minh:

a, (x+y).(x\(^2\)-xy+y\(^2\))=\(x^3\)+\(y^3\)

b, (x+y)\(^3\)= \(x^3+3x^2y+3xy^2+y^3\)

mong m.n giúp đỡ nhiều

Answer 1

a: \(\left(x+y\right)\left(x^2-xy+y^2\right)\)

\(=x^3-x^2y+xy^2+x^2y-xy^2+y^3\)

\(=x^3+y^3\)

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

\(=\left(x+y\right)\left(x^2+2xy+y^2\right)\)

\(=x^3+2x^2y+xy^2+2x^2y+2xy^2+y^3\)

\(=x^3+3x^2y+3xy^2+y^3\)

Answer 2

a. Ta có \(\left(x+y\right)\left(x^2-xy+y^2\right)=x^3-x^2y+xy^2+x^2y-xy^2+y^3=x^3+y^3\)

\(\Rightarrow\left(x+y\right)\left(x^2-xy+y^2\right)=x^3+y^3\)

b. Ta có \(x^3+3x^2y+3xy^2+y^3=x^3+y^3+3xy\left(x+y\right)=\left(x+y\right)\left(x^2-xy+y^2\right)+3xy\left(x+y\right)=\left(x+y\right)\left(x^2+2xy+y^2\right)=\left(x+y\right)\left(x+y\right)^2=\left(x+y\right)^3\)\(\Rightarrow\left(x+y\right)^3=x^3+3x^2y+3xy^2+y^3\)