Question

What is Multiplication of Monomials by Polynomials?

Answer 1

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`