Question

Phân tích đa thức thành  nhân tử:

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

b) \(\left(x^2-8\right)^2+36\)

c) \(81x^4+4\)

Answer 1

b)\(\left(x^2-8\right)^2+36\)

\(=x^4-16x^2+100\)

\(=x^4+20x^2+100-36x^2\)

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

\(=\left(x^2-6x+10\right)\left(x^2+6x+10\right)\)

Answer 2

c)81x⁴+4

=81x⁴+36x²+4-36x²

=(9x²+2)²-(6x)²

=(9x²+6x+2)(9x²-6x+2)

Answer 3

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

\(=\left(x^2+2x-1\right)^2\)