Binomial Expansion Basics
Ever wondered how to expand something like ^8 without multiplying it out eight times? Binomial expansion is your answer, and it works for three main types of expressions.
The binomial theorem gives us a shortcut to expand any binomial raised to a power. Instead of multiplying a+b$$a+b$$a+b... repeatedly, we can use patterns to write out the answer directly.
Pascal's triangle is brilliant for finding coefficients. Each row gives you the numbers you need - just start with 1 at the top, then each number below is the sum of the two numbers above it. Row 4 gives you 1, 4, 6, 4, 1 for expanding something to the power of 4.
When expanding ^n, the powers of 'a' start at n and decrease by 1 each term, whilst the powers of 'b' start at 0 and increase by 1 each term. The coefficients come straight from Pascal's triangle.
Quick tip: The row number in Pascal's triangle matches the power you're expanding to!
