All I wanted to do was cube (8+x) and I got every answer eg derivative except the one I wanted!
Expand the following:
(x + 8)^3
(x + 8)^3 | = | sum_(k=0)^3 binomial(3, k) x^(3 - k)×8^k |
| = | binomial(3, 0) x^3 8^0 + binomial(3, 1) x^2 8^1 + binomial(3, 2) x^1 8^2 + binomial(3, 3) x^0 8^3 | : invisible comma
binomial(3, 0) x^3 + 8 binomial(3, 1) x^2 + 64 binomial(3, 2) x + 512 binomial(3, 3)
The binomial coeffients comprise the 4^th row of Pascal's triangle:
=1 | | 3 | | 3 | | 1
x^3 + 3 8 x^2 + 3 8^2 x + 8^3
8^2 = 64:
x^3 + 8 3 x^2 + 64 3 x + 8^3
8^3 = 8×8^2:
x^3 + 8 3 x^2 + 64 3 x + 512
8^2 = 64:
x^3 + 8 3 x^2 + 64 3 x + 64 8
8×64 = 512:
x^3 + 8 3 x^2 + 64 3 x + 512
64×3 = 192:
x^3 + 8 3 x^2 + 192 x + 512
8×3 = 24:
x^3 + 24 x^2 + 192 x + 512
