What is Multiplication of Monomials by Polynomials?

1 Answer
KillerBunny
Feb 1, 2015

It works the same as with numbers. For numbers, you know that #a(b+c)# equals #ab+ac#.
For the same reason, if you have a monomial and you want to multiplicate it by a polynomial (which is a sum of monomials with some coefficients!), you follow the same rule.

For example, if your monomial is #3x^2#, and your polynomial is #3+2x-5x^2+8x^3#, the product is
#3x^2(3+2x-5x^2+8x^3)#
you will calculate is as
#3x^2\cdot 3+3x^2\cdot2x-3x^2\cdot5x^2+3x^2\cdot8x^3#, which is
#9x^2 + 6x^3 - 15x^4 + 24x^5#

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