How to Multiply Three Binomials?

Binomial is actually a type of polynomial. When there are two terms in a polynomial, it will be referred to binomial. Binomials can also be obtained by summing up two monomials. Multiplication of three binomials can be easily obtained. Binomials are those algebraic expressions which are comprised of two monomials. Binomials are considered as simplest type of Polynomials. Monomial can be defined as expression that may consist of base, variable and exponent. Here we will discuss how to multiply three binomials.

1)     First of all, take first two binomials and rewrite them.

2)     Simple Multiplication of first terms of both binomials is performed. (multiply the bases and add the exponents (powers).

3)     Then multiply the first term of first binomial with second term of second binomial.

4)     In the next step, second term of first binomial is multiplied with first term of second binomial.

5)     Finally multiply both second terms of two binomials. Whole multiplication will have result of multiplication of two binomials.

6)     Now take third binomial and multiply each of the term of obtained result with each of the term of third binomial. Thus required result will be obtained.

Let’s take an example (a + 5) (a + 3) (a + 2),
Here take first two polynomials (a + 5) (a + 3) and multiply terms as per steps, it gives
(a + 5) (a + 3) = a² + 8a + 15.
Now multiply the obtained result with third polynomial as shown below:
(a2 + 8a + 15) (a + 2) = (a2) (a + 2) + (8a) (a + 2) + (15) (a + 2),
                                    = a³ + 2 a² + 8a² + 16a + 15a + 30,
                                    = a³ + 10 a² + 31a + 30.