Question

phân tích đa thức thành hình nhân tử 

1 .  \(x^2\)-2x + 1 - xy - y

2 . \(x^3-4x^2\)+ 4x - 2x + 2

3 . 10x - 25 - \(x^2+4y^2\)

4 . \(4x^2\)- 2x + 2xy -y

5 . 4x \(\left(x-3\right)^2-3x^2\)+ 9x

 

 

Answer 1

\(1.\)

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

\(2.\)

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

\(3.\)

\(10x-25-x^2+4y^2=4y^2-\left(x^2-10x+25\right)=4y^2-\left(x-5\right)^2=\left(2y+x-5\right)\left(2y-x+5\right)\)

\(4.\)

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

\(5.\)

\(4x\left(x-3\right)^2-3x^2+9x=4x\left(x-3\right)^2-3x\left(x-3\right)=\left(x-3\right)\left(4x^2-12x-3x\right)\)