Question

phân tích đa thức thành nhân tử:

a, 5x^2- 10x= 5      b, -3x^2+ 6xy-  3y^2         c, a^2-b^2+ 2a- 2b      d, x^3-6x^2y+9xy^2

Answer 1

\(a,5x^2-10x+5\)
\(=5\left(x^2-2x+1\right)\)
\(=5\left(x-1\right)^2\)
______________________
\(b,-3x^2+6xy-3y^2\)
\(=-3\left(x^2-2xy+y^2\right)\)
\(=-3\left(x-y\right)^2\)
_______________________
\(c,a^2-b^2+2a-2b\)
\(=\left(a-b\right)\left(a+b\right)+2\left(a-b\right)\)
\(=\left(a-b\right)\left(a+b+2\right)\)
_______________________
\(d, x^3-6x^2y+9xy^2\)
\(=x\left(x^2-6x^2y+9y^2\right)\)
\(=x\left(x-3y\right)^2\)

Answer 2

`a)5x^2-10x+5=5(x^2-2x+1)=5(x-1)^2`

`b)-3x^2+6xy-3y^2=-3(x^2-2xy+y^2)=-3(x-y)^2`

`c)a^2-b^2+2a-2b=(a-b)(a+b)+2(a-b)=(a-b)(a+b+2)`

`d)x^3-6x^2y+9xy^2=x(x^2-6xy+9y^2)=x(x-3y)^2`