Multiplying monomials review

CCSS Math: HSA.APR.A.1
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 2x2x or 7y7y. 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.
(4x2)(7x3){(-4x^2)(7x^3)}
When a number is next to a variable, it means they are multiplied. So,
(4x2)(7x3)(\blueD{-4}\maroonD{x^2})(\blueD{7}\maroonD{x^3})
is the same as
(4)(x2)(7)(x3)(\blueD{-4})(\maroonD{x^2})(\blueD{7})(\maroonD{x^3}).
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).
(4)(7)(x2)(x3)\blueD{(-4)(7)}\maroonD{(x^2)(x^3)}
Then simplify, and we're done!
28x5\blueD{-28}\maroonD{x^5}

Example 2

Simplify.
(8a2)(5a6){(-8a^2)(-5a^6)}
When a number is next to a variable, it means they are multiplied. So,
(8a2)(5a6)(\blueD{-8}\maroonD{a^2})(\blueD{-5}\maroonD{a^6})
is the same as
(8)(a2)(5)(a6)(\blueD{-8})(\maroonD{a^2})(\blueD{-5})(\maroonD{a^6}).
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).
(8)(5)(a2)(a6)\blueD{(-8)(-5)}\maroonD{(a^2)(a^6)}
Then simplify, and we're done!
40a8\blueD{40}\maroonD{a^8}
Want to see another example? Check out this video.

Practice

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