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If there is subtracting terms in either polynomial, change them to adding a negative. Each term in the first polynomial is multiplied by each term in the 2nd polynomial, then add all the resulting terms together (taking into account the signs of the resulting multiplications), simplify by combining like powers of the variable.

This is basically what you are doing when you multiply 2 numbers by hand, example: 997 x 42 = 41874

997

x 42

----- First you mutiply 2 x 7 = 14, put the 4 carry the 1, etc.

Imagine instead (4x + 2)(9x2 + 9x + 7) = 2*7 + 2*9*x + 2*9*x2 + (4*x)*7 + (4*x)*(9*x) + (4*x)*(9x2) = 14 + 46x + 54x2 + 36x3

For x = 10 --> 14 +460 + 5400 + 36000 = 41874.

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Q: What is the rules in multiplying polynomials?
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