What is the binomial expansion of #(x + 2y)^7#?

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Answer 1 · 2015-06-19T14:07:48

#(x+2y)^7=#

#x^7+14x^6y+84x^5y^2+280x^4y^3+560x^3y^4+672x^2y^5+448xy^6+128y^7#

Choose the 8th row of Pascal's triangle to get the sequence:

#1, 7, 21, 35, 35, 21, 7, 1#

Write the powers of #2# in ascending order up to #2^7# as a sequence:

#1, 2, 4, 8, 16, 32, 64, 128#

Multiply the two sequences together to get:

#1, 14, 84, 280, 560, 672, 448, 128#

Then:

#(x+2y)^7 =#

#x^7+14x^6y+84x^5y^2+280x^4y^3+560x^3y^4+672x^2y^5+448xy^6+128y^7#