(x + 1)6 – (x – 1)6
(x + 1)6 – (x – 1)6
Above terms can be written as,
((x + 1)3)2 – ((x – 1)3)2
We know that, (a2 – b2) = (a + b) (a – b)
[(x + 1)3 + (x – 1)3] [(x + 1)3 – (x – 1)3]= [(x + 1) + (x – 1)][(x + 1)2 – (x – 1) (x + 1) + (x – 1)2] [(x + 1) – (x – 1)][(x + 1)2 + (x – 1) (x + 1) + (x – 1)2]
(x + 1 + x – 1) [x2 + 2x + 1 – x2 + 1 + x2 + 1 – 2x(x + 1) – x + 1] [x2 + 2x + 1 + x2 – 1 + x2 – 2x + 1]
By simplifying we get,
2x(x2 + 3) 2(3x2 + 1)
4x(x2 + 3) (3x2 + 1)