Cumulative Standards Review
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(a+b)n = P0anb0 + P1an−1b + … + Pn−1abn−1 + Pna0bn |
It can be shown that the ith coefficient of the nth row of the Pascal's Triangle equals nCi. Therefore, we can restate the binomial theorem using combinations.
(a+b)n = nC0anb0 + nC1an−1b + … + nCn−1abn−1 + nCna0bn |
(a+b)n=P0anb0+P1an−1b1+⋯+Pn−1a1bn−1+Pna0bn |
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(x+2y)6=1x6(2y)0+6x5(2y)1+15x4(2y)2+20x3(2y)3+15x2(2y)4+6x1(2y)5+1x0(2y)6 |
a0=1
a1=a
a⋅1=a
(a⋅b)m=am⋅bm
Calculate power
Multiply
6C0=0!(6−0)!6!
Subtract terms
Cancel out common factors
Simplify quotient
0!=1
aa=1