Multiplying Algebraic Expressions

Multiplying Variables with Exponents

You might need to be able to multiply variables with exponents on the GED math test.  For example

n² x n³ = ?

You can’t just find what n² and n³ are and then multiply them, as you would with a number. This is because you don’t know what n is. The way you multiply variables with exponents is actually by adding up the exponents and keeping the variable the same.

Remember you can only multiply variables with exponents with the same variables with exponents. You cannot multiply, for example, n² with x³ since n and x are different exponents.

Distributing Products When Multiplying Paranthesis

There is a special process you need to go through when multiplying a term by an expression in parentheses. For example, how do you do this:

3n(5n +7)

Of course when something is immediately next to something in parentheses that means multiplication, but which part of the expression in parentheses do you multiply it by since 5n+ 7 can’t be simplified further? The answer is both parts.

If there are three terms in the parentheses, you need to multiply whatever is outside by all three terms, and so on.

2n(3n² + 2n – 4)

Multiplying an Expression in Parentheses by an Expression in Parentheses

If you need to multiply two parentheses that both contain two terms you need to make sure you multiply each term in both parentheses with both terms in the other parentheses. For example:

(n + 2)(n – 5)

The order you multiply the terms in is often referred to as the FOIL method:

First two terms

Outside two terms

Inside two terms

Last two terms


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  • deep

    can you please tell me more about the foil method?

    • Ziyi

      Sure, no problem. When I get some time I’ll make a video explaining it, which will hopefully be helpful.

      • Anonymous

        Can you help me understand the foil method. I take the GED math test gor the last time. I need as much help I can get at this point

  • summer camps san francisco

    Write down the number of days in a week you’d like to go out for a dinner
    Double it
    Add 5
    Multiply by 50
    If you have had your birthday this year add 1760, if not add 1759
    Subtract the year you were born in
    You should have a 3 digit number
    The last two digits are your age…

    How come this works?
    any algebraic expression?

    • Alexander

      Its Wrong i did it and yes of course i got the 3 digit number but the last 2 digits are wrong it said i was 20 im 22 already so i added 1760 to it and got me the WRONG ANSWER!!!!!

      • Megan Trotter

        I did that and I only got a two digit number saying 19 I am 20 I only wanted to go out to dinner twice a week so if I had said 3 it would have been spot on but i still would have had two digits 😛 i guess it just depends on the preson and what yer there where born and all that good stuff.

        • Jeremy

          Good joke on us, suumer camps san francisco. Your little algebra trick doesn’t work. Hah!

    • Nessaward Narcotic

      I did that and got 315 and I’m 18 not 15 lol but I enjoyed this lol

    • mook

      I think you have to add 1 to 1760/1759 for each year since it was posted(2012)…or not–just tried it still 2 years off.

  • the don


    • Nova


  • Llo

    Just want to point out that in this sentence:
    “You cannot multiply, for example, n² with x³ since n and x are different exponents.”

    n and x are, of course, different *variables.* 🙂

    Great site!

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