Question

phân tích đa thức sau thành nhân tử

a)x⁴+4x²-5

b)-x-y²+x²-y

c)x(x+y)-5x-5y

d)x²-5x+5y-y²

e)5x³-5x²y-10x²+10xy

f)27x³-8y³

Answer 1

a) \(x^4+4x^2-5=x^4+4x^2+4-9=\left(x^2+2\right)^2-3^2\)

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

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

c) \(x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)

d) \(x^2-5x+5y-y^2=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y-5\right)\)

e) \(5x^3-5x^2y-10x^2+10xy=5x^2\left(x-y\right)-10x\left(x-y\right)\)

\(=5\left(x-y\right)\left(x^2-2x\right)\)

f) \(27x^3-8y^3=\left(3x\right)^3-\left(2y\right)^3=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)