Question

How many terms are there in the expansion of (x + y)¹00?

A) 100
B) 101
C) 200
D) 201

Answer 1

The expansion of (x + y)100 has 101 terms.

Step-by-step explanation:

The expansion of the expression (x + y)100 can be found using the binomial theorem. The binomial theorem states that (a + b)n = nC0anb0 + nC1an-1b1 + nC2an-2b2 + ... + nCna0bn, where nCk is the binomial coefficient.

For the expression (x + y)100, n = 100 and a = x, b = y. Plugging these values into the binomial theorem formula, we get 100C0x100y0 + 100C1x99y1 + 100C2x98y2 + ... + 100C100x0y100.

There are 101 terms in the expansion, so the correct answer is (B) 101.