Question

(X+5) to the power 6 use binomial theorem to expand the power of a binomial

Answer 1

x⁶ +30x⁵ +375x⁴ +2500x³ +9375x² +18750x +15625

Explanation:

The expansion is the sum of C(6, k)·x^(6-k)·5^k for k=0–6, where ...

... C(6, k) = 6!/(k!(6-k)!)

For k = 0–6, C(6, k) = {1, 6, 15, 20, 15, 6, 1}

Then the expansion is ...

... x⁶ +6·5¹·x⁵ +15·5²·x⁴ +20·5³·x³ +15·5⁴·x² +6·5⁵·x +5⁶