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Question

Chứng minh đẳng thức:

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

b)$\left(a+b\right)\left(a^2-ab+b^2\right)=a^3+b^3$

Cảm ơn mn trước nha!

Nguyễn Kim Hưng · Accepted Answer

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

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

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

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

b)$\left(a+b\right)\left(a^2-ab+b^2\right)$

$=a^3-a^2b+ab^2+a^2b-ab^2+b^3$

$=a^3+b^3+\left(-a^2b+a^2b\right)+\left(ab^2-ab^2\right)$

$\Rightarrow$$\left(a+b\right)\left(a^2-ab+b^2\right)=a^3+b^3$Câu trả lời: a)$\left(x-y\right)\left(x^4+x^3y+x^2y^2+xy^3+y^4\right)$

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

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

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

b)$\left(a+b\right)\left(a^2-ab+b^2\right)$

$=a^3-a^2b+ab^2+a^2b-ab^2+b^3$

$=a^3+b^3+\left(-a^2b+a^2b\right)+\left(ab^2-ab^2\right)$

$\Rightarrow$$\left(a+b\right)\left(a^2-ab+b^2\right)=a^3+b^3$

Ngẫu Hứng · Answer

a) (x - y)(x4 + x3y + x2y2 + xy3 + y4)

= x(x4 + x3y + x2y2 + xy3 + y4) - y(x4 + x3y + x2y2 + xy3 + y4)

= x5 + x4y + x3y2 + x2y3 + xy4 - x4y - x3y2 - x2y3 - xy4 - y5

= x5 - y5

b) (a + b)(a2 - ab + b2)

= a(a2 - ab + b2) + b(a2 - ab + b2)

= a3 - a2b + ab2 + a2b - ab2 + b3

= a3 + b3Câu trả lời: a) (x - y)(x4 + x3y + x2y2 + xy3 + y4)