Q:

# What are the steps in multiplying polynomials with exponents?

A:

The steps for multiplying polynomials with exponents vary depending on the complexity of the polynomials. If the equation has only one variable, the answer can be found by multiplying the individual terms, combining the terms with the same degree and simplifying.

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When multiplying two-term polynomials, the FOIL method is used. The FOIL acronym stands for First Outer Inner Last. It describes the order in which the terms of the two polynomials are multiplied. For example, given the equation (a^2 + 4)(2a + 5), the first two terms are multiplied first: a^2 x 2a = 2a^3. Next the outer terms are multiplied: a^2 x 5 = 5a^2. Next the inner terms are multiplied: 4 x 2a = 8a. Finally the last terms are multiplied: 4 x 5 = 20. Combine terms where possible, and arrange them in descending order of degree: 2a^3 + 5a^2 + 8a + 20.

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