Question

Find -3a^2 - b^3 + 3c^2 - 2b^3 if a = 2, b = -1, and c = 3.

Answer 1

Calculated with Mathematica 9 Home Edition.

Answer 2

If you want to see the steps involved:\[-3a^2-b^3+3c^2-2b^3\]Collect like terms first:
\[-3a^2-b^3-2b^3+3c^2 = -3a^2 - 3b^3+3c^2\]Now substitute in our values of \(a=2,\,b=-1,\,c=3\):
\[-3(2)^2-3(-1)^3+3(3)^2 = -3(4)-3(-1)^3+3(9) \]\((-1)^n\) is \(1\) if \(n\) is even, and \(-1\) if \(n\) is odd. \(3\) is odd, so \((-1)^3 = -1\)
\[-3(4)-3(-1)+3(9) = -12 +3 + 27 = -12 + 30 = 30 - 12 = 18\]