Binomials are those algebraic expressions which are comprised of two monomials. Binomials are considered as the 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. Given below are the steps to multiply three binomials:
- First of all, take first two binomials and rewrite them.
- Simple multiplication of first terms of both binomials is performed. (Multiply the bases and add the exponents)
- Then, multiply the first term of the first binomial with the second term of the second binomial.
- In the next step, second term of the first binomial is multiplied with the first term of the second binomial.
- Finally, multiply both the second terms of two binomials. Whole multiplication will have result of multiplication of two binomials.
- Now, take third binomial and multiply each term of obtained result with each of the term of the third binomial. Thus, the required result will be obtained.
Let us take an example $(a + 5) (a + 3) (a + 2)$.
Here, take first two polynomials $(a + 5) (a + 3)$ and multiply the terms as per steps given above.
$(a + 5) (a + 3) = a^2 + 8a + 15$
Now, multiply the obtained result with the third polynomial as shown below:
$(a^2 + 8a + 15) (a + 2) = (a^2) (a + 2) + (8a) (a + 2) + (15) (a + 2)$
= $a^3 + 2a^2 + 8a^2 + 16a + 15a + 30$
= $a^3 + 10a^2 + 31a + 30$