Objectives :
1. Be able to tell if you can use the "HCF" method to solve expressions.
2. Be able to solve expressions using the method.
3. Be able to tell what is Factoring with the highest common factor is.
What does factorizing with the Highest Common Factor mean?
Factorizing expressions can be done using two methods; These methods are called:
HCF and Difference of Two Squares.
The HCF method is when you use the "Highest Common Factor" (HCF) to factorize the terms.
How to solve expressions using the HCF method :
Example 1 :
20x - 10
Step 1: Identify the Highest common factor(s) in the expression.
Step 2: Write down the highest common factor(s) that you have collected.
Step 3: Use the HCF(s) to factor out the terms in the expression.
Step 4: Place the factored terms in a bracket leaving the HCF(s) on the outside.
Written Example:
20x - 10
10 - HCF
10/20 = 10
10/10 = 1
10( 2x - 1 )
Example 2:
12mn + 18mp
Step 1: Identify the Highest common factor(s) in the expression.
Step 2: Write down the highest common factor(s) that you have collected.
Step 3: Use the HCF(s) to factor out the terms in the expression.
Step 4: Place the factored terms in a bracket leaving the HCF(s) on the outside.
Written Example:
12mn + 18mp
6m = HCF
6m/12mn = 2n
6m/ 18mp = 3p
6m ( 2n + 3p )
As shown in the written example above the "6m" was common in both expressions and so we began the calculation.
"6m" into "12mn" is equal to "2n"
"6m" into "18mp" is equal to "3p"
You read in the step-by-step explanation that you should rewrite the factored terms in brackets and leave the "HCF" on the outside of the bracket.
Those procedures were followed and hence we ended up with the answer being " 6m ( 2n + 3p ) "
Even though the procedure appears to be simple students often make mistakes when solving the expression so, here I will share some mistakes often made and tips on how to reduce them.
Common mistakes often made by students :
1. Don't find the Highest common factor correctly.
2. They don't factor out the terms properly.
Ways to fix these common mistakes :
1. Make sure you take a good look at the terms and choose the one(s) that is the HIGHEST and COMMON.
2. When factoring out the terms make sure you factor out the common terms leaving only the uncommon ones.
Here is a fun activity for you to try:
If you haven't checked out our step by step guide on how to solve an expression using the difference of two squares you can always feel free to check out our page titled :
"STEP BY STEP GUIDE ON HOW TO FACTORIZE USING THE DIFFERENCES OF TWO SQUARES + DIAGRAMS"
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