Question

Factor x^5y^2+x^2y^5

Answer 1

The answer is

x²y²( x + y)(x² - xy + y²)

Explanation:

`{x}^(5) {y}^(2) + {x}^(2) {y}^(5)`

To factorize the expression first factor

x²y² out

We have

x²y²( x³ + y³)

Using the expression

a³ + b³ = ( a + b)(a² - ab + b²)

Factorize the terms in the bracket

So we have

x³ + y³ = ( x + y)(x² - xy + y²)

Combine the expressions

We have the final answer as

x²y²( x + y)(x² - xy + y²)

Hope this helps you

Answer 2

x^2y^2(x+y)(x^2-xy+y^2)

Explanation:

x^5y^2+x^2y^5

Factor out the greatest common factor

x^2y^2( x^3+y^3)

Apply the Sum of Cubes Formula x^3+y^3 =(x+y)(x^2-xy+y^2)

x^2y^2(x+y)(x^2-xy+y^2)