Question

phân tích đa thức thành nhân tử

(x² + 4y² - 20)² - 16(xy - 4)²

Answer 1

\(\left(x^2+4y^2-20\right)^2-16\left(xy-4\right)^2=\left(x^2+4y^2-20\right)^2-\left(4xy-16\right)^2=\left(x^2+4y^2-20-4xy+16\right)\left(x^2+4y^2-20+4xy-16\right)=\left[\left(x-2y\right)^2-4\right]\left[\left(x+2y\right)^2-36\right]=\left(x-2y-2\right)\left(x-2y+2\right)\left(x+2y-6\right)\left(x+2y+6\right)\)

Answer 2

\(\left(x^2+4y^2-20\right)^2-\left(4xy-16\right)^2\)

\(=\left(x^2+4y^2-20-4xy+16\right)\left(x^2+4y^2-20+4xy-16\right)\)

\(=\left[\left(x-2y\right)^2-4\right]\left[\left(x+2y\right)^2-36\right]\)

\(=\left(x-2y-2\right)\left(x-2y+2\right)\left(x+2y-6\right)\left(x+2y+6\right)\)