Question

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

Answer 1

Answer:

$x(x+y)^2$

Step-by-step 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

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

$xy(x+y)^2=x\times y\times (x+y)^2$

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

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

$2x(x+y)^2=2\times x\times (x+y)^2$

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

$=x(x+y)^2$