How to Multiply Binomials

How to Multiply Binomials

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The phrase "binomial," as the name implies, is made up of the terms "bi" and "nomial," which relate to a variety of expressions. A binomial is an algebraic or mathematical phrase consisting of two terms linked by a mathematical operation. Furthermore, the binomial terms may include constants, variables, or a mixed term with a co-efficient. Furthermore, the variable's power (let's say $x$) in a binomial should be an integer, not a fractional power like the squared or cube root.
For example, $2x^{\frac{1}{3}} \ + \ 3x$ is not a binomial as the first term has a fraction power of $x$.

Degree of a Binomial

Unlike a polynomial, the degree of a binomial is pretty simple to find. Since a binomial consists of only two terms, hence its degree would obviously be the greatest exponent power of that variable. So, for example in the term $4x^3 \ + \ 3x^2$, we can see that the greatest degree of $x$ is $3$. So, the degree of the binomial is considered as $3$.
Now, for a binomial expression with multiple variables, the case becomes quite complex. So, for example, let’s take the multivariable binomial expression $3x^2y^3 \ + \ 4x^3$. Now, here we can clearly see that the binomial has 2 different variables as $x$ and $y$. So, what we do here is add up the exponent powers of the separate variables. So, in this case the addition comes as $2 \ + \ 3 \ = \ 5$. Hence, the degree of this monomial is $5$ (we do not consider the degree of $4x^3$ i.e., $3$ since it is lower than the multivariable term degree).

Multiplying Binomials

While multiplying binomials, take note of the following steps:

• When you are multiplying binomials, always remember the exponents rule. Multiplication always leads to addition of exponent terms of the same variables.
• Next, you should always use the distributive property while multiplying binomial.
• Next, apply the FOIL rule which is First Out Last In.

Let’s understand the multiplication of binomials by the following example:

• $(−9x \ − \ 1)(−4x \ + \ 4) \ = \ 36x^2 \ + \ (−36)x \ + \ 4x \ + \ (−4) \ = \ 36x^2 \ − \ 32x \ – \ 4$

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