Question

Phân tích thành nhân tử : \(\left(1+x^2\right)^2-4x\left(1-x^2\right)\)

Answer 1

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

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

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

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

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

Answer 2

( 1  + x²)²  -  4x ( 1 - x² )  

= x⁴ + 2x² + 1 - 4x + 4x³

= x³ + 2x² - x + 2x³  + 4x² - 2x - x²  - 2x + 1

= x ( x² + 2x -  1 ) +  2x  ( x²  + 2x - 1 ) - ( x² + 2x  - 1 ) 

= ( x² + 2x - 1 ) ( x² + 2x   - 1 ) 

= ( x² +  2x - 1)²