How to Multiply 2 Polynomials

A polynomial is a term that can have any combination of numbers, letters and exponents. In order for an expression to be a polynomial, the exponents must be whole numbers, and the values within the expression must be added, subtracted or multiplied together. Polynomials have a long history in algebra, as well as other branches of sciences such as chemistry and physics. Multiplying polynomials is not difficult, but there are rules to remember.

Things You'll Need

• Calculator (optional)

Instructions

How to multiply two polynomials

1. Multiply coefficients together and add exponents on like bases together. In the example 3 (4a + b), each expression within the parentheses is multiplied by the 3 out front. The solution for this example, therefore, is 12a + 3b. In the example a(3a^2+b), the expressions inside the parentheses are multiplied by the "a" out front, but in the first expression 3a^2, the exponents on the "a's" are added together. The solution for this example, therefore, is 3a^3 + ab.

2. Multiply each value of the polynomial to every other value in the polynomial. For example, in 3a (5 + b), the 3a must be multiplied by the 5, then the b, then added together to get 15a + 3ab.

3. Multiply the coefficients and add the exponents- distributing each expression in the first polynomial with each expression in the second. For example, in 3a^2b^3 (4ac + b^2) the 3 in the first term should be multiplied to both of the terms within parentheses. Then the exponents of each letter term should be added together. The solution for this more complex problem, therefore, is 12a^3c + 3a^2b^5.