What is the Binomial Expansion of $(2+x)^4$ ?

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Answer 1 · 2015-06-29T20:30:19

$(2+x)^4 = 16+32x+24x^2+8x^3+x^4$

Write out the 5th row of Pascal's triangle as a sequence:

$1, 4, 6, 4, 1$

Write out the powers of $2$ from $2^4$ down to $2^0$ :

$16, 8, 4, 2, 1$

Multiply the two sequences together to get:

$16, 32, 24, 8, 1$

These are the coefficients of the binomial expansion:

$(2+x)^4 = 16+32x+24x^2+8x^3+x^4$

What is the Binomial Expansion of (2+x)^4(2+x)^4?