Question

Let a^6 - b^6 is simplified to (a - b) (a^2 - ab + b^2) k , then k is?

Let `a^6` - `b^6` is simplified to (a - b) (`a^2` - ab + `b^2`) k, then k is?

Answer 1

The solution is `k=(a+b)(a^2+ab+b^2)`.

Explanation:

`a^6-b^6=(a-b)(a^2-ab+b^2)k`

`(a^3)^2-(b^3)^2=(a-b)(a^2-ab+b^2)k`

Difference of squares factoring:

`(a^3-b^3)(a^3+b^3)=(a-b)(a^2-ab+b^2)k`

Difference of cubes factoring:

`(a-b)(a^2+ab+b^2)(a^3+b^3)=(a-b)(a^2-ab+b^2)k`

`color(red)cancelcolor(black)((a-b))(a^2+ab+b^2)(a^3+b^3)=color(red)cancelcolor(black)((a-b))(a^2-ab+b^2)k`

`(a^2+ab+b^2)(a^3+b^3)=(a^2-ab+b^2)k`

Sum of cubes factoring:

`(a^2+ab+b^2)(a+b)(a^2-ab+b^2)=(a^2-ab+b^2)k`

`(a^2+ab+b^2)(a+b)color(red)cancelcolor(black)((a^2-ab+b^2))=color(red)cancelcolor(black)((a^2-ab+b^2))k`

`(a^2+ab+b^2)(a+b)=k`

`k=(a+b)(a^2+ab+b^2)`

That's the answer. Hope this helped!