# Pls. help me factor these given, i'm new to factoring,  a raised to 9 minus b raised to 9   a^9 - b^9the ^ sign is exponent, thx

giorgiana1976 | Student

This is the difference of two cubes and it returns the product:

`a^(9)` - `b^(9)` = `a^(3*3)` - `b^(3*3)` = (`a^(3)` -`b^(3)` )(`a^(3*2)` + `a^(3)`*`b^(3)` + `b^(3*2)` )

`a^(9)` - `b^(9)` = (`a^(3)` - `b^(3)` )(`a^(6)` + `a^(3)` *`b^(3)` + `b^(6)` )

We notice that the 1st factor is also a difference of two cubes:

`a^(9)` - `b^(9)` = (a - b)(`a^(2)` + ab + `b^(2)` )(`a^(6)` + `a^(3)`*`b^(3)` + `b^(6)` )

The factorized expression is `a^(9)` - `b^(9)` = (a-b)(`a^(2)` + ab + `b^(2)` )(`a^(6)` + `a^(3)` *`b^(3)` + `b^(6)` ).

neela | Student

We can use the identity.

x^3-y^3 = (x-y)(x^2+xy+y^2).

Therefore a^9-b^9 could be written as x^3-y^3, where x = a^3 and y = b^3.

So a^9-b^9 = (a^3)^3-(b^3)^3 = (a^3-b^3)(a^6+a^3b^3+b^6) = (a-b)(a^2+ab+b^2)﻿(a^6+a^3b^3+b^6).

Therefore a^3-b^3 = (a-b)(a^2+ab+b^2)﻿(a^6+a^3b^3+b^6).

sunaabh | Student

a<b so x>y same here