1
Question
Factorise
(a+b)3+(a-b)3+6a(a2-b2)
Factorise
(a+b)3+(a-b)3+6a(a2-b2)
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Solution
1) Expand
(a+b)3+(a-b)^3+6a(a2-b2)
(α³+2α²b+αb²+bα²+2b²α+b³)+(α³−2α²b+αb²−bα²+2b²α−b³)+(6α³−6αb²)
Gather like terms
(α³+α³+6α³)+(2α²b+α²b−2α²b−α²b)+(αb²+2αb²+αb²+2αb²−6αb²)+(b³−b³) =
(8α³)+(3α²b-3α²b)+(6αb²−6αb²)+(b³−b³)
Simplify
8α³
(a+b)3+(a-b)^3+6a(a2-b2)
(α³+2α²b+αb²+bα²+2b²α+b³)+(α³−2α²b+αb²−bα²+2b²α−b³)+(6α³−6αb²)
Gather like terms
(α³+α³+6α³)+(2α²b+α²b−2α²b−α²b)+(αb²+2αb²+αb²+2αb²−6αb²)+(b³−b³) =
(8α³)+(3α²b-3α²b)+(6αb²−6αb²)+(b³−b³)
Simplify
8α³
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