SOLUTION: Algebra help!! (2x-3)^4

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Question 654549: Algebra help!! (2x-3)^4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Look at Row 5 in Pascals triangle: 1, 4, 6, 4, 1

These are the coefficients to the terms

(2x)^4*(-3)^0
(2x)^3*(-3)^1
(2x)^2*(-3)^2
(2x)^1*(-3)^3
(2x)^0*(-3)^4

Note: you basically raise the first piece to the 4th power and the second piece to the 0th power. Then you count down on the first exponent and count up on the second exponent.

so we get

1*(2x)^4*(-3)^0
4*(2x)^3*(-3)^1
6*(2x)^2*(-3)^2
4*(2x)^1*(-3)^3
1*(2x)^0*(-3)^4

which simplifies to

1*(16x^4)*(1)
4*(8x^3)*(-3)
6*(4x^2)*(9)
4*(2x^1)*(-27)
1*(1)*(81)

and that simplifies to

16x^4
-96x^3
216x^2
-216x
81

Now add up the terms to get

16x^4 - 96x^3 + 216x^2 - 216x + 81

So

(2x-3)^4 = 16x^4 - 96x^3 + 216x^2 - 216x + 81 for all values of x