Question

phân tích đa thức thành nhân tử: ( x²-2x+2)⁴ + 20x^2(x² -2x+2)²+64x⁴

^{giúp mình với nhé}

Answer 1

\(\left(x^2-2x+2\right)^4+20x^2\left(x^2-2x+2\right)+64x^4\)

=\(\left[\left(x^2-2x+2\right)^4+2.10x^2\left(x^2-2x+2\right)^2+100x^4\right]\)-100x⁴+64x²

=\(\left[\left(x^2-2x+2\right)^2+10x^2\right]^2-36x^2\)

=\(\left[\left(x^2-2x+2\right)^2+4x^2\right].\left[\left(x^2-2x+2\right)^2+16x^2\right]\)