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:

$(x+2y)^7 =$

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

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