*John Hamilton*Show bio

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.

Instructor:
*John Hamilton*
Show bio

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

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.

- For more homeschool information related to mathematics, feel free to visit our Homeschool Curriculum.

**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

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(3
*a*+ 2) = 6*a*+ 4 - -2(3
*a*+ 2) = -6*a*- 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) = ?

A fractional exponent is one such as *a*1/2, which is really just another way of writing ''the square root of *a*''. On the other hand, *a*1/3 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/*a*1/2 or ''1 divided by the square root of *a*''.

Can you solve this problem?

**Problem #2**

*a*-1/5 = ?

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

2*a*(*a*2 + 3*a* - 5) = 2*a*3 + 6*a*2 - 10a

It's your turn again.

**Problem #3**

3*a*(*a*3 - 2*a*2 + 4*a* - 1) = ?

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) (2*a*+ 2) = ? - 2
*a*2 + 2*a*+ 6*a*+ 6 = - 2
*a*2 + 8*a*+ 6

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

- First - multiply
*a*times 2*a*to get 2*a*2 - Outer - multiply
*a*times 2 to get 2*a* - Inner - multiply 3 times 2
*a*to get 6*a* - 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) (3*b* + 8) = ?

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

Prepare your own worksheet in which you show all your work on these problems, and then apply the answers to a similar real-world scenario, such as preparing recipes in the kitchen and having to double or halve the ingredients. On the other hand, as a mechanical engineer, you would utilize your polynomials to design your new favorite thrilling roller coaster.

For another illustration, if you were a zoologist you might use your aforementioned *a*-1/5 exponent to measure your pet bat's wingspan. Furthermore, NASA astronauts often use algebra to determine how much breathable air is contained in spacesuits.

To demonstrate your knowledge of how to perform algebraic distributions, you could:

- Create a podcast or video explaining the concepts to other persons
- Design a poster containing relevant information from this assignment, including polynomials, fractional along with negative exponents, as well as positive and negative integers

Create in your mind's eye an algebra board game you can play with your family and schoolmates.

**Problem #1**

-3(*a* - 3) = -3a + 9

In this case, remember a negative number times a negative number equals a positive number.

**Problem #2**

*a*-1/5 = 1/*a*1/5 or ''1 divided by the fifth root of a''

**Problem #3**

- 3
*a*(*a*3 - 2*a*2 + 4*a*- 1) = - 3
*a*4 - 6*a*3 + 12*a*2 - 3*a*

Be sure not to make any careless sign errors during your calculations.

**Problem #4**

- (
*b*- 2) (3*b*+ 8) = ? - 3
*b*2 + 8*b*- 6*b*- 16 = - 3
*b*2 + 2*b*- 16

Requirements | 0-5 points |
---|---|

Define above three key terms | |

Show how to distribute positive and negative integers | |

Solve fractional and negative exponents | |

Distribute a polynomial | |

Explain FOIL | |

Give a presentation to an adult | |

Total: |
/30 |

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