Question

phân tích đa thức thành nhân tử

a)\(x^2-2x-4y^2-4y\)

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

c.\(x^2\left(1-x^2\right)-4-4x^2\)

Answer 1

a )\(x^2-2x-4y^2-4y=\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)

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

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

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

c ) \(x^2\left(1-x^2\right)-4-4x^2=x^2-x^4-4-4x^2\)

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

Answer 2

a.x²-2x-4y²-4y=(x²-4y²)-(2x+4y)=(x-2y)(x+2y)-2(x+2y)=(x+2y)(x-2y-2)

b.x⁴+2x³-4x-4=(x⁴-4)+(2x³-4x)=(x²-2)(x²+2)+2x(x²-2)=(x²-2)(x²+2x+2)

c.x²(1-x²)-4-4x²= -x⁴-3x²-4=x²-(x⁴+4x²+4)=x²-(x²+2)²=(x-x²-2)(x+x²+2)