How do you find the binomial expansion of (x2y)6?

1 Answer
Jun 6, 2015

Use Pascal's triangle and choose the row that starts with 1,6, that is:

1,6,15,20,15,6,1

Write out the powers of 2 up to 26 as a sequence:

1,2,4,8,16,32,64

Multiply the two sequences together:

1,12,60,320,480,192,64

Alternate the signs:

1,12,60,320,480,192,64

Hence:

(x2y)6

=x612x5y+60x4y2320x3y3+480x2y4192xy5+64y6