Question

Phân tích đa thức thành nhân tử: \(-8x^6-60x^4y-150x^2y^2-125y^3\)

Answer 1

\(-8x^6-60x^4y-150x^2y^2-125y^3\)

\(=-\left(8x^6+60x^4y+150x^2y^2+125y^3\right)\)

\(=-\left[\left(2x^2\right)^3+3\cdot\left(2x^2\right)^2\cdot5y+3\cdot2x^2\cdot\left(5y\right)^2+\left(5y\right)^3\right]\)

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

Answer 2

$-8x^6-60x^4y-150x^2y^2-125y^3$

$=-(8x^6+125y^3)-(60x^4y+150x^2y^2)$

$=-[(2x^2)^3+(5y)^3]-30x^2y(2x^2+5y)$

$=-(2x^2+5y)(4x^4-10x^2y+25y^2)-30x^2y(2x^2+5y)$

$=(2x^2+5y)(-4x^4+10x^2y-25y^2-30x^2y)$

$=(2x^2+5y)(-4x^4-20x^2y-25y^2)$

$=-(2x^2+5y)^3$