How do you use pascals triangle to expand (3y-4x)^4?

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Answer 1 · 2015-08-04T23:04:10

Write out the 5th row of Pascal's triangle multiply it by sequences of descending powers of $3$ and ascending powers of $-4$ to get:

$(3y-4x)^4 = 81y^4-432y^3x+864y^2x^2-768yx^3+256x^4$

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

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

Write down powers of $3$ in descending order from $3^4$ to $3^0$ as a sequence:

$81$ , $27$ , $9$ , $3$ , $1$

Multiply these two sequences together to get:

$81$ , $108$ , $54$ , $12$ , $1$

Write down powers of $-4$ in ascending order from $4^0$ to $4^4$ as a sequence:

$1$ , $-4$ , $16$ , $-64$ , $256$

Multiply these last two sequences together to get:

$81$ , $-432$ , $864$ , $-768$ , $256$

These are the coefficients of our terms, giving:

$(3y-4x)^4 = 81y^4-432y^3x+864y^2x^2-768yx^3+256x^4$