Câu hỏi của Cao Tùng Lâm

Question

Chứng minh rằng: (x – y)(x4 + x

Tô Mì · Accepted Answer

$\left(x-y\right)\left(x^4+x^3y+x^2y^2+xy^3+y^4\right)=x^5-y^5$

Ta có VT:

$\left(x-y\right)\left(x^4+x^3y+x^2y^2+xy^3+y^4\right)$

$=x.x^4+x.x^3y+x.x^2y^2+x.xy^3+x.y^4-y.x^4-y.x^3y-y.x^2y^2-y.xy^3-y.y^4$

$=x^5+x^4y+x^3y^2+x^2y^3+xy^4-x^4y-x^3y^2-x^2y^3-xy^4-y^5$

$=x^5-y^5$

VT=VP
Vậy:...

Câu trả lời:

$\left(x-y\right)\left(x^4+x^3y+x^2y^2+xy^3+y^4\right)=x^5-y^5$

Ta có VT:

$\left(x-y\right)\left(x^4+x^3y+x^2y^2+xy^3+y^4\right)$

$=x.x^4+x.x^3y+x.x^2y^2+x.xy^3+x.y^4-y.x^4-y.x^3y-y.x^2y^2-y.xy^3-y.y^4$

$=x^5+x^4y+x^3y^2+x^2y^3+xy^4-x^4y-x^3y^2-x^2y^3-xy^4-y^5$

$=x^5-y^5$

VT=VP
Vậy:...