Question

phân tích đa thức

a)x^4+4

4x^4+4x^2y^2-8y^4

Answer 1

\(x^4+4\)

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

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

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

\(4x^4+4x^2y^2-8y^4\)

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

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

\(=4\left[x^2\left(x^2-y^2\right)+2y^2\left(x^2-y^2\right)\right]\)

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

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

Answer 2

a) \(x^4+4=x^4+4x^2+4-4x^2\)

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

b) \(4x^4+4x^2y^2-8y^4=4x^4+4x^2y^2+y^4-9y^4\)

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

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

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