Question

How many terms are in the simplified expansion of (x+y)4?
A) 4
B) 8
C) 16
D) 32

Answer 1

The expansion of (x+y)^4 can be found using the binomial theorem formula, which simplifies to 5 terms.

Step-by-step explanation:

The expansion of (x+y)^4 can be found using the binomial theorem formula, which states that (a+b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n, where nCk represents the binomial coefficient of n choose k.

In this case, n = 4, so the expansion is:

1. nC0 * x^4 * y^0
2. nC1 * x^3 * y^1
3. nC2 * x^2 * y^2
4. nC3 * x^1 * y^3
5. nC4 * x^0 * y^4

Calculating the binomial coefficients, the expansion simplifies to: