Question

phân tích đa thức thành nhân tử

a,x^2+6xy+9y^2 4a^4-4a^2b^2+b^4 x^6+y^2-2x^3y

b,(x+y)^3-(x-y)^3 25x^4-10x^2y^2+y^4 -a^2-2a-1

c,27b^3-8a^3 x^3+9x^y+27xy^2+27y^3 16x^2-9(x+y)^2

Answer 1

a: \(x^2+6xy+9y^2=\left(x+3y\right)^2\)

b: \(4a^4-4a^2b^2+b^4=\left(2a^2-b^2\right)^2\)

\(x^6-2x^3y+y^2=\left(x^3-y\right)^2\)

b: \(\left(x+y\right)^3-\left(x-y\right)^3\)

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

\(=2y\left(3x^2+y^2\right)\)

\(25x^4-10x^2y^2+y^4=\left(5x^2-y^2\right)^2\)

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