Factoring a Difference of Squares
A difference of squares takes on the form
In mathematics, difference means subtraction, so in order to fit this form, two perfect squares MUST be subtracted.
The rule for factoring a difference of squares is:
The rule for factoring a difference of squares is:
Here are some steps to follow when factoring using a difference of squares.
Remember, if there was a GCF, you should include it in your final answer!
Again, you can check that you factored correctly by FOIL/the distributive property.
- Check for a GCF - if there is one, factor like you did in the last lesson, if there is not, move to step 2
- Make two sets of parentheses, one with an addition sign and the other with a subtraction sign (it does not matter which comes first): ( + )( - )
- Take the square root of the first term and write it in the first position of both sets of parentheses
- Take the square root of the second term and write it in the second position of both sets of parentheses
Remember, if there was a GCF, you should include it in your final answer!
Again, you can check that you factored correctly by FOIL/the distributive property.
Here is an example:
Step 1: Check for a GCF.
There is not a greatest common factor (other than 1), so we move on to step 2.
Step 2: Make two sets of parentheses, one with an addition sign and the other with a subtraction sign
There is not a greatest common factor (other than 1), so we move on to step 2.
Step 2: Make two sets of parentheses, one with an addition sign and the other with a subtraction sign
Step 3: Take the square root of the first term and write it in the first position of both sets of parentheses
Step 4: Take the square root of the second term and write it in the second position of both sets of parentheses
Remember you can check to make sure you factored correctly by using FOIL.
Here is another example:
Step 1: Check for a GCF.
The greatest common factor is 3, so factoring out the GCF we get:
The greatest common factor is 3, so factoring out the GCF we get:
Step 2: Make two sets of parentheses, one with an addition sign and the other with a subtraction sign. Be sure to bring down the GCF!
Step 3: Take the square root of the first term and write it in the first position of both sets of parentheses.
Step 4: Take the square root of the second term and write it in the second position of both sets of parentheses.
Remember you can check to make sure you factored correctly by using FOIL and the distributive property.
Watch the following video to learn more about factoring using the difference of squares. Pay close attention to the warning - if it is a sum, you cannot factor.
Practice:
Use the following websites to practice factoring difference of squares:
https://za.ixl.com/math/grade-9/factorise-quadratics-differences-of-squares
http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/diff_of_squares/diff_of_squares_practice.html
https://za.ixl.com/math/grade-9/factorise-quadratics-differences-of-squares
http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/diff_of_squares/diff_of_squares_practice.html
Quick Check:
Complete the following quick check. When you are finished (and have mastered) the difference of squares, move onto "AC Method for Quadratics."
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