Multiplication
Polynomial by a Polynomial
Let’s start by multiplying two binomials, a polynomial with two terms. The Distributive Property also applies in this situation.
Example Multiply & simplify.
(2x + 3)(4x2 + 5)
Step 1. Multiply each term in the first binomial through the second binomial.
2x(4x2 + 5) + 3(4x2 + 5)
Step 2. Continue to use the Distributive Property on the two new terms.
(2x)(4x2) + (2x)(5) + (3)(4x2) + (3)(5)
Step 3. Multiply the monomials in each term.
8x3 + 10x + 12x2 + 15
Step4. Combine like terms if needed and write in standard form.
8x3 + 12x2 + 10x + 15
What you should notice is that when multiplying any two polynomials, every term in one polynomial is multiplied by every term in the other polynomial.