Answer: 6a^3-6a^2b+3ab-3b^2
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Work Shown:
(2a^2+b)(3a-3b)
c(3a-3b) ..... let c = 2a^2+b
3ac-3bc .... distribute
3a(c)-3b(c)
3a(2a^2+b)-3b(2a^2+b) .... plug in c = 2a^2+b
3a(2a^2)+3a(b)-3b(2a^2)-3b(b) ... distribute
6a^3+3ab-6a^2b-3b^2
6a^3-6a^2b+3ab-3b^2
You could also use the FOIL rule to get the same result. The box method is a visual way to keep track of the terms.