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Focus I: Raising Polynomials to Any Power

Test yourself (Answers)

(3x - 2)5 = 5C0(3x)5 + 5C1(3x)4(-2) + 5C2(3x)3(-2)2 + 5C3(3x)2(-2)3 + 
                        5C4(3x)(-2)4 + 5C5(-2)5

You can calculate the combinations using the formula or you can read them from row 5 of Pascal's Triangle. Either way you should end up with:

(3x - 2)5 = 1(3x)5 + 5(3x)4(-2) + 10(3x)3(-2)2 +10(3x)2(-2)3 + 5(3x)(-2)4 + 1(-2)5 

(3x - 2)5 = 243x5 - 810x4 + 1080x3 - 720 x2 + 240x - 32

Note the sign change depending on whether the negative term is raised to an odd or even power.