Question

Phân tích đa thức thành nhân tử

x² + y² - x²y² + xy - x + y

a(b² + c² + bc) + b(c² +a² + ac) + c(a² + b² + ab)

a(a + 2b)³ - b(2a +b)³

Answer 1

b: \(=ab^2+ac^2+abc+bc^2+ba^2+abc+a^2c+b^2c+abc\)

\(=ab\left(a+b+c\right)+bc\left(a+b+c\right)+ac\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left(ab+bc+ac\right)\)

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

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

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

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

\(=\left(1-y\right)\cdot\left[y\left(x-1\right)\left(x+1\right)+x\left(x-1\right)\right]\)

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