Question

Phân tích đa thức thành nhân tử

1) \(\left(x^2+1\right)^2-4x^2\).

2) \(x^2-y^2+2yz-z^2\)

Giúp Mk nha Mk tk

Answer 1

a) Đưa về hằng đẳng thức số 3 , ta có :

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

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

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

b) \(x^2-y^2+2yz-z^2\)

\(=x^2-\left(y^2-2yz+z^2\right)\)

\(=x^2-\left(y-z\right)^2\)

Tương tự như câu a , áp dụng hằng số 3 , ta có :

\(=x^2-\left(y-z\right)^2=\left(x-y+z\right)\left(x+y-z\right)\)

Answer 2

1) \(\left(x^2+1\right)^2-4x^2\)

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

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

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

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

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

Answer 3

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

            = ( x -1)² . ( x + 1)²

2 )   .... =  x² - ( y² - 2yz + z² )

            = x² - ( y - z )²

            = ( x - y + z ).( x + y - z )

Answer 4

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

\(x^2-y^2+2yz-z^2=x^2-\left(y^2-2yz+z^2\right)=x^2-\left(y-z\right)^2=\left( x+y-z\right)\left(x-y+z\right)\)