Câu hỏi của Phan Hoàng Linh Ngọc

Question

Phân tích đa thức thành nhân tử
a,a6-a4+2a3+2a2

b,(a+b+c)3-(a+b-c)3-(b+c-a)3-(c+a-b)3

Lưu Hạ Vy · Accepted Answer

$a^6-a^4+2a^3+2a^2$

$\Rightarrow a^2.\left(a^4-a^2+2a+2\right)$

$\Rightarrow$ $a^2.\left(a^2.\left(a^2-1\right)+2\left(a+1\right)\right)$

$\Rightarrow a^2.\left(a^2.\left(a-1\right).\left(a+1\right)+2\left(a+1\right)\right)$

$\Rightarrow a^2.\left(a+1\right)\left(a^2.\left(a-1\right)+2\right)$

$\Rightarrow a^2.\left(a+1\right).\left(a^3-a^2+2\right)$

$\Rightarrow a^2.\left(a+1\right).\left(a^3+a^2-2a^2+2\right)$

$\Rightarrow a^2.\left(a+1\right).\left(a^2.\left(a+1\right)-2\left(a^2-1\right)\right)$

$\Rightarrow a^2.\left(a+1\right).\left(a^2.\left(a+1\right)-2\left(a-1\right).\left(a+1\right)\right)$

$\Rightarrow a^2.\left(a+1\right).\left(a+1\right).\left(a^2-2\left(a-1\right)\right)$

$\Rightarrow a^2.\left(a+1\right).\left(a+1\right).\left(a^2-2a+2\right)$

$\Rightarrow a^2.\left(a+1\right)^2.\left(a^2-2a+2\right)$Câu trả lời: $a^6-a^4+2a^3+2a^2$