Question

Help
Factor.

8x9−27y15

Answer 1

(2x^3 - 3y^5) • (4x^6 + 6x^3y^5 + 9y^10)

Answer 2

The factored form is
`8x^9-27y^(15)=(2x^3-3y^5)(4x^6+6x^3y^5+9y^(10)`

Explanation:

Given : Expression
`8x^9-27y^(15)`

To find : Factor the expression ?

Solution :

Re-write expression as

`8x^9-27y^(15)=(2x^3)^3-(3y^5)^3`

Applying identity,
`a^3-b^3=(a-b)(a^2+ab+b^2)`

Here,
`a=2x^3` and
`b=3y^5`

`8x^9-27y^(15)=(2x^3-3y^5)((2x^3)^2)+(2x^3)(3y^5)+(3y^5)^2`

`8x^9-27y^(15)=(2x^3-3y^5)(4x^6+6x^3y^5+9y^(10)`

Therefore, The factored form is
`8x^9-27y^(15)=(2x^3-3y^5)(4x^6+6x^3y^5+9y^(10)`