Question

phân tích nhân tử 4xy(x^2+y^2)-6(x^3+y^3+x^2y+xy^2)+9(x^2+y^2) giúp mình với thank

Answer 1

\(4xy\left(x^2+y^2\right)-6\left(x^3+y^3+x^2y+xy^2\right)+9\left(x^2+y^2\right)\)

\(=4xy\left(x^2+y^2\right)-6\left[x\left(x^2+y^2\right)+y\left(x^2+y^2\right)\right]+9\left(x^2+y^2\right)\)

\(=4xy\left(x^2+y^2\right)-6\left(x^2+y^2\right)\left(x+y\right)+9\left(x^2+y^2\right)\)

\(=\left(x^2+y^2\right)\left(4xy-6x-6y+9\right)\)

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

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