Question

phân tích đa thức thành nhân tử

a. (1 + x²)² - 4x (1 - x²)

b. (x² - 8)² + 36

Answer 1

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

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

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

\(=\left(x^2-8-6\right)\left(x^2-8+6\right)\)

\(=\left(x^2-14\right)\left(x^2-2\right)\)

Answer 2

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

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

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

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

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

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

=\(\left(x^2-8-6\right)\left(x^2-8+6\right)=\left(x^2-14\right)\left(x^2+2\right)\)(trừ 36 nhé)