Question

1)Rút gọn bt

a)3x²(x+1)(x-1)-(x²-1)(x⁴+x²+1)+(x²-1)³

b)(x+y+z)³+(x-y-z)³+(y-x-z)³+(z-y-x)³

2)Phân tích đa thức thành nhân tử:

(x-1)(x+2)(x+3)(x+6)-6(x²+5x)²+45

Answer 1

1)

a) \(=3x^2\left(x^2-1\right)-\left(x^3-1\right)+x^8-3x^4+3x^2-1\)

\(=3x^4-3x^2-x^3+1+x^8-3x^4+3x^2-1=x^8-x^3\)

2) 

\(=\left(x^2+5x-6\right)\left(x^2+5x+6\right)-6\left(x^2+5x\right)+45\)

\(=\left(x^2+5x\right)^2-6\left(x^2+5x\right)-36+45\)

\(=\left(x^2+5x\right)^2-6\left(x^2+5x\right)+9=\left(x^2+5x-3\right)^2\)