Question

Phân tích đa thức sau thành phân tử;

\(a,16x^4+y^4+4x^2y^2\)

\(b,x^3-2x-4\)

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

Answer 1

a ) \(16x^4+y^4+4x^2y^2=\left(4x^2\right)^2+8x^2y^2+y^4-4x^2y^2=\left(4x^2+y^2\right)^2-\left(2xy\right)^2=\left(4x^2+y^2-2xy\right)\left(4x^2+y^2+2xy\right)\)

b ) \(x^3-2x-4\)

\(=\left(x^3-8\right)-2x+4\)

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

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

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

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

\(=\left(x^3+8\right)+\left(x^2-4\right)\)

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

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

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