Binomial Expansion (AQA A-Level Mathematics): Flashcards

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Binomial Expansion
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Binomial coefficient formula (nk)\binom{n}{k}

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

Number of terms in (a+b)n(a+b)^n expansion

n+1n + 1

Sum of exponents in each term of (a+b)n(a+b)^n

nn

Pascal's Triangle rule for each number

Sum of the two directly above it

Sign pattern in (ab)n(a-b)^n expansion

Signs alternate

Factorial n!n! definition

Product of all positive integers up to nn

Powers of aa in (a+b)n(a+b)^n expansion

Decrease from ana^n to a0a^0

Powers of bb in (a+b)n(a+b)^n expansion

Increase from b0b^0 to bnb^n

Calculate (42)\binom{4}{2}

66

Requirement for nn in basic binomial expansion

Non-negative integer

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