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Multiplying monomials review

A monomial is a polynomial with just one term. For example, 2a^5 is a monomial. This article reviews how to multiply monomials (e.g., 2a^5 * 3a^2 = 6a^7).
A monomial is a polynomial with just one term, like 2, x or 7, y. Multiplying monomials is a foundational skill for being able to multiply binomials and polynomials more generally, so it's good to review a few examples.

Example 1

Simplify.
left parenthesis, minus, 4, x, squared, right parenthesis, left parenthesis, 7, x, cubed, right parenthesis
When a number is next to a variable, it means they are multiplied. So,
left parenthesis, start color #11accd, minus, 4, end color #11accd, start color #ca337c, x, squared, end color #ca337c, right parenthesis, left parenthesis, start color #11accd, 7, end color #11accd, start color #ca337c, x, cubed, end color #ca337c, right parenthesis
is the same as
left parenthesis, start color #11accd, minus, 4, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, x, squared, end color #ca337c, right parenthesis, left parenthesis, start color #11accd, 7, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, x, cubed, end color #ca337c, right parenthesis.
Now we can rearrange the factors because multiplication is commutative (a fancy way of saying that the order in which we multiply things doesn't matter).
start color #11accd, left parenthesis, minus, 4, right parenthesis, left parenthesis, 7, right parenthesis, end color #11accd, start color #ca337c, left parenthesis, x, squared, right parenthesis, left parenthesis, x, cubed, right parenthesis, end color #ca337c
Then simplify, and we're done!
start color #11accd, minus, 28, end color #11accd, start color #ca337c, x, start superscript, 5, end superscript, end color #ca337c

Example 2

Simplify.
left parenthesis, minus, 8, a, squared, right parenthesis, left parenthesis, minus, 5, a, start superscript, 6, end superscript, right parenthesis
When a number is next to a variable, it means they are multiplied. So,
left parenthesis, start color #11accd, minus, 8, end color #11accd, start color #ca337c, a, squared, end color #ca337c, right parenthesis, left parenthesis, start color #11accd, minus, 5, end color #11accd, start color #ca337c, a, start superscript, 6, end superscript, end color #ca337c, right parenthesis
is the same as
left parenthesis, start color #11accd, minus, 8, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, a, squared, end color #ca337c, right parenthesis, left parenthesis, start color #11accd, minus, 5, end color #11accd, right parenthesis, left parenthesis, start color #ca337c, a, start superscript, 6, end superscript, end color #ca337c, right parenthesis.
Now we can rearrange the factors because multiplication is commutative (a fancy way of saying that the order in which we multiply things doesn't matter).
start color #11accd, left parenthesis, minus, 8, right parenthesis, left parenthesis, minus, 5, right parenthesis, end color #11accd, start color #ca337c, left parenthesis, a, squared, right parenthesis, left parenthesis, a, start superscript, 6, end superscript, right parenthesis, end color #ca337c
Then simplify, and we're done!
start color #11accd, 40, end color #11accd, start color #ca337c, a, start superscript, 8, end superscript, end color #ca337c
Want to see another example? Check out this video.

Practice

Problem 1
Simplify.
left parenthesis, 7, h, cubed, right parenthesis, left parenthesis, 3, h, start superscript, 7, end superscript, right parenthesis

Want more practice? Check out this exercise. Also check out this challenge exercise.

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