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

Question

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

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Answer 1 · 2018-03-20T23:20:15

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

#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#

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

#(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#

#(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!