Question

Factor
81x^6-25y^10
Explanation too please

Answer 1

`(9x^3+5y^5)(9x^3-5y^5)`

Explanation:

`81x^6-25y^(10)`

`81=9^2`

`x^6=x^(3 \cdot 2)=(x^3)^2`

`\implies 81x^6=(9x^3)^2`

`25=5^2`

`y^(10)=y^(5 \cdot 2)=(y^5)^2`

`\implies 25y^(10)=(5y^5)^2`

Therefore,

`81x^6-25y^(10)=(9x^3)^2 -(5y^5)^2`

Apply difference of two squares formula
`x^2-y^2=(x+y)(x-y)`:

`\implies (9x^3)^2 -(5y^5)^2=(9x^3+5y^5)(9x^3-5y^5)`