Binomial Expansion
Expand powers of binomials and find terms efficiently.
The binomial theorem gives a fast way to expand \((a+b)^n\).
Binomial theorem\[(a+b)^n=\sum_{r=0}^{n}\binom{n}{r}a^{n-r}b^r\]
Worked example
Expand \((x+2)^4\).
\[(x+2)^4=x^4+4x^3(2)+6x^2(2^2)+4x(2^3)+2^4\]\[=x^4+8x^3+24x^2+32x+16\]Finding a specific term
The general term is \(\binom nr a^{n-r}b^r\). Use this instead of expanding everything when the question asks for one coefficient.