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

Let a^6a6 - b^6b6 is simplified to (a - b) (a^2a2 - ab + b^2b2) k, then k is?

1 Answer
Mar 20, 2018

The solution is k=(a+b)(a^2+ab+b^2)k=(a+b)(a2+ab+b2).

Explanation:

a^6-b^6=(a-b)(a^2-ab+b^2)ka6b6=(ab)(a2ab+b2)k

(a^3)^2-(b^3)^2=(a-b)(a^2-ab+b^2)k(a3)2(b3)2=(ab)(a2ab+b2)k

Difference of squares factoring:

(a^3-b^3)(a^3+b^3)=(a-b)(a^2-ab+b^2)k(a3b3)(a3+b3)=(ab)(a2ab+b2)k

Difference of cubes factoring:

(a-b)(a^2+ab+b^2)(a^3+b^3)=(a-b)(a^2-ab+b^2)k(ab)(a2+ab+b2)(a3+b3)=(ab)(a2ab+b2)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!