Question

Use the binomial theorem to expand (a^(2)-3)^(4). Show your work

Answer 1

a^8 - 12a^6 + 54a^4 - 108a^2 + 81.

Explanation:

General form of the binomial theorem:

( a + b)^n = a^n + nC1 a^(n-1)b + nC2 a^(n - 2)b^2 +.......... + b^n

So:

(a^2 - 3)^4 = (a^2)^4 + 4C1 (a^2)^3*(-3) + 4C2 (a^2)^2 (-3)^2 + 4C3 (a^2) (-3)^3

+ (-3)^4

= a^8 + 4 * a^6 * -3 + 6 * a^4 * 9 + 4 * a^2 * -27 + 81

= a^8 - 12a^6 + 54a^4 - 108a^2 + 81.