What is the binomial expansion of ${(x + 2)}^{5}$ $(x+2)^5$ ?

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Answer 1 · 2015-07-19T12:42:07

${(x + 2)}^{5} = x^{5} + 10 x^{4} + 40 x^{3} + 80 x^{2} + 80 x + 32$ $(x+2)^5 = x^5+10x^4+40x^3+80x^2+80x+32$

Write out the $6$ $6$ th row of Pascal's triangle as a sequence:

$1, 5, 10, 10, 5, 1$ $1, 5, 10, 10, 5, 1$

Write out ascending powers of $2$ $2$ from $2^{0}$ $2^0$ up to $2^{5}$ $2^5$ as a sequence:

$1, 2, 4, 8, 16, 32$ $1, 2, 4, 8, 16, 32$

Multiply the two sequences together to get:

$1, 10, 40, 80, 80, 32$ $1, 10, 40, 80, 80, 32$

These are the coefficients of the expansion:

${(x + 2)}^{5} = x^{5} + 10 x^{4} + 40 x^{3} + 80 x^{2} + 80 x + 32$ $(x+2)^5 = x^5+10x^4+40x^3+80x^2+80x+32$

What is the binomial expansion of (x+2)^5(x+2)5(x+2)^5?