Question

nài 3: phân tích đa thức dau thành nhân tử

a, x⁴+2x²+1

b,4x²-12xy+9y²

c,-x²-2xy-y²

d,(x+y)²-2(x+y)-1

e, x³-3x²-3x-1

g,x³+6x²+12x+8

h,x³+1-x²-x

k,(x+y)³-x³-y³

Answer 1

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

\(b,4x^2-12xy+9y^2=\left(2x-3y\right)^2\)

\(c,-x^2-2xy-y^2=-\left(x^2+2xy+y^2\right)=-\left(x+y\right)^2\)

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

Answer 2

e: \(x^3-3x^2+3x-1=\left(x-1\right)^3\)

g: \(=\left(x+2\right)^3\)

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

k: \(=x^3+y^3+3xy\left(x+y\right)-x^3-y^3\)

=3xy(x+y)