How do you use pascals triangle to expand $(2s+1)^4$ ?

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Answer 1 · 2015-07-17T21:12:30

Combine the 5th row of Pascal's triangle with descending powers of $2$ to find:

$(2s+1)^4 = 16s^4+32s^3+24s^2+8s+1$

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

$1$ , $4$ , $6$ , $4$ , $1$

Write out powers of $2$ in descending order from $2^4$ to $2^0$ :

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

Multiply these two sequences together to get:

$16$ , $32$ , $24$ , $8$ , $1$

These are the coefficients of the powers of $s$ in the expansion:

$(2s+1)^4 = 16s^4+32s^3+24s^2+8s+1$

How do you use pascals triangle to expand (2s+1)^4(2s+1)^4?