Binomial Theorem Flashcardizz

The Binomial Theorem provides a formula for expanding expressions of the form (a + b)^n, where n is a non-negative integer. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

$$a^2 + 2ab + b^2$$ .

x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1.

1, 7, 21, 35, 35, 21, 7, 1.

$$a^5 - 5a^4b + 10a^3b^2 - 10a^2b^3 + 5ab^4 - b^5$$ .

The general term is given by T(k+1) = (n choose k) * a^(n-k) * b^k.

(n choose k) or C(n, k) represents the number of ways to choose k elements from a set of n elements without regard to the order of selection.

(1 + x)^0 = 1.

(1 + x)^1 = 1 + x.

The coefficient of x^3 is 10 * (2^3) * (3^2) = 10 * 8 * 9 = 720.