How do you find the binomial expansion of #(x-2y)^6#?

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Answer 1 · 2015-06-06T10:57:28

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 #2^6# 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:

#(x - 2y)^6#

#=x^6-12x^5y+60x^4y^2-320x^3y^3+480x^2y^4-192xy^5+64y^6#