Question

X^3y+2x^2y^2+xy^3 and 2x^3+4x^2y+2xy^2 Find the HCF.​

Answer 1

`x(x+y)^2`

Explanation:

We are given that

`x^3y+2x^2y^2+xy^3` and
`2x^3+4x^2y+2xy^2`

We have to find HCF.

`x^3y+2x^2y^2+xy^3=xy(x^2+2xy+y^2)`

=
`xy(x+y)^2`

By using the formula

`(x+y)^2=x^2+2xy+y^2`

`xy(x+y)^2=x* y* (x+y)^2`

`2x^3+4x^2y+2xy^2=2x(x^2+2xy+y^2)`

`=2x(x+y)^2`

`2x(x+y)^2=2* x* (x+y)^2`

HCF of (
`x^3y+2x^2y^2+xy^3,2x^3+4x^2y+2xy^2`)

`=x(x+y)^2`