Question

`x^4 +1`

`4x^4 y^4 +1`

`x^4 +3x^2 +4`

`x^2 +3xy+2y^2`

phân tích thành nhân tử

Answer 1

\(x^4+1\)

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

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

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

______

\(4x^4y^4+1\)

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

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

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

______

\(x^4+3x^2+4\)

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

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

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

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

______

\(x^2+3xy+2y^2\)

\(=x^2+xy+2xy+2y^2\)

\(=x\left(x+y\right)+2y\left(x+y\right)\)

\(=\left(x+2y\right)\left(x+y\right)\)