Binomial Expansion (AQA A-Level Mathematics): Quizzes

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Binomial Expansion
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For the Binomial Theorem (a+b)n(a+b)^n, what type of number must nn be?

Non-negative integer

What is the formula for the binomial coefficient (nk)\binom{n}{k}?

n!k!(nk)!\frac{n!}{k!(n-k)!}

In (a+b)n(a+b)^n, as terms progress, powers of aa _____ and powers of bb _____.

decrease; increase

How many terms are in the expansion of (a+b)n(a+b)^n?

n+1n+1

In Pascal's Triangle, how is each number formed?

Sum of two directly above it

What is (31)\binom{3}{1} in the expansion of (x+1)3(x+1)^3?

3

How do signs behave in the expansion of (ab)n(a-b)^n?

Signs alternate

In each term of (a+b)n(a+b)^n, what is the sum of the exponents of aa and bb?

nn

Calculate (42)\binom{4}{2} using the formula.

6

What happens to binomial expansion with fractional or negative exponents?

Becomes an infinite series

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