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#