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Multiplying polynomials by monomials

Multiplying polynomials by monomials is simple. The following examples will help you to multiply polynomials.

Multiplying a polynomial by a monomial

Simple example.

Multiplying a polynomial by a monomial:

2x(5x + 6y)

Each term multiplied by the monomial 2x:

2x(5x + 6y) =
2x5x + 2x6y =
10x2 + 12xy

Multiplying polynomial with 2 variables by a monomial

Example.

Multiplying polynomial with 2 different variables by a monomial:

2a(20x2 + 17xy - 10y2)

How to resolve the problem?

Each term multiplied by the monomial 2a:

2a*20x2 + 2a*17xy + 2a*(-10y2) =
40ax2 + 34axy - 20ay2