Question

Factor the monomial.

$40m^{2}n$

Short answer

The factor of the monomial is $40m^{2}n=2\times 2\times 2\times 5\times m\times m\times n$.

Step-by-step solution

  Define monomials

A monomial is an expression that has a single term, with variables and a coefficient. For example, $2xy$ is a monomial since it is a single term, has two variables, and one coefficient.

  State the concept to factor the monomial

To factor a monomial completely, write the coefficient as a product of primes and expand the variable part.

Step 3   Factor the monomial

First, expand and separate the variables from its coefficients.

$\text{40}|{\text{m}}^{2}n$

In the next step, expand each individually-

$40m^{2}n=2\times 2\times 2\times 5\times m\times m\times n$