Câu hỏi của Nhẽo Nhạt

Question

Tính (x^3-y^3)-(x^3+y^3) Giúp mình với!!

Quốc Đạt · Accepted Answer

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

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

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

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

$\Leftrightarrow x^3+3x^2y+3xy^2+y^3-3x^2y-3xy^2-x^3+3x^2y-3xy^2+y^3-3x^2y+3xy^2$

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

$\Leftrightarrow2y^3$Câu trả lời: $\left(x^3-y^3\right)-\left(x^3+y^3\right)$

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

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

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

$\Leftrightarrow x^3+3x^2y+3xy^2+y^3-3x^2y-3xy^2-x^3+3x^2y-3xy^2+y^3-3x^2y+3xy^2$

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

$\Leftrightarrow2y^3$

Violympic toán 8