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There's another way to do these -- it might help you keep better track of the details.

Remember how to multiply this guy by hand?

DO IT!

239 x 46 =

 

Well, we can just stack the polynomials and do it the same way!

Check it out:

( 4x^2 - 2x + 6 ) ( x + 3 ) = 12x^2 - 6x + 18 + 4x^3 - 2x^2 + 6x = 4x^3 + 10x^2 + 0x + 18 = 4x^3 + 10x^2 + 18

I call this the "stacking" method.