Algebra I Assignment - Performing Algebraic Distribution

Instructor: John Hamilton

John has tutored algebra and SAT Prep and has a B.A. degree with a major in psychology and a minor in mathematics from Christopher Newport University.

This homeschool assignment demonstrates how to perform algebraic distribution involving both positive and negative integers, including exponents and polynomials. This assignment is suitable for students who are in the ninth grade. Updated: 01/29/2021

Algebraic Distribution Assignment Explanation and Topic Overview

Algebra! Just hearing the dreaded word spoken aloud can cause a 9th grade student to break out in a cold sweat. Don't worry, though. Learning algebra is just like learning to ride a bicycle or learning a new dance, as it just takes some patience, perseverance, and practice to accomplish the given task at hand.

Your students will benefit from this homeschool assignment by learning the basics of distributing algebra terms.

Key Terms

  • Distribution: multiplication of algebra terms located both inside and outside of parentheses
  • Term: a number, variable, or the two multiplied to form one expression
  • Variable: a letter that represents an unknown number you are trying to find


  • Internet access
  • Paper for performing math calculations
  • Worksheets with algebra problems
  • Writing implements


  • One day to complete these algebra problems
  • One week to create a presentation

Assignment Instructions for Students

Step One - Distributing Positive and Negative Integers

Let's begin! First of all, you can use algebraic distribution to solve equations with both positive and negative integers.

Now, please note distribution is different when using positive versus negative integers. Let's take a look:

  • 2(3a + 2) = 6a + 4
  • -2(3a + 2) = -6a - 4

See the difference? In the second example, you literally distribute the negative to both numbers in the parentheses.

Now you try.

  • Note - The answers and explanations are at the bottom of the assignment. Try to solve all problems the first time without using a calculator.

Problem #1

-3(a - 3) = ?

Step Two - Fractional and Negative Exponents

A fractional exponent is one such as a1/2, which is really just another way of writing ''the square root of a''. On the other hand, a1/3 is really just another way of writing ''the cube root of a''.

A negative exponent is one such as a-1/2, which is really just another way of writing 1/a1/2 or ''1 divided by the square root of a''.

Can you solve this problem?

Problem #2

a-1/5 = ?

Step Three - Polynomials

Distributing a term over polynomials is similar to what we just did in Step One of this assignment. For instance:

2a(a2 + 3a - 5) = 2a3 + 6a2 - 10a

It's your turn again.

Problem #3

3a(a3 - 2a2 + 4a - 1) = ?

Step Four - FOIL

Let's talk about a cool little ''trick'', which is actually a reliable math rule, you will need to use as you improve your algebra skills.

The important acronym you need to memorize is FOIL, which stands for First, Outer, Inner, Last, when performing certain math operations. For instance, let's solve:

  • (a + 3) (2a + 2) = ?
  • 2a2 + 2a + 6a+ 6 =
  • 2a2 + 8a + 6

That wasn't too bad, was it? To review what we just did:

  • First - multiply a times 2a to get 2a2
  • Outer - multiply a times 2 to get 2a
  • Inner - multiply 3 times 2a to get 6a
  • Last - multiply 3 times 2 to get 6

Then we simply combined like terms to get the final answer. Now you solve one.

Problem #4

(b - 2) (3b + 8) = ?


Have an online contest between fellow students to see who can solve one dozen algebra equations the quickest.

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