This week in Math 10 we learned about factoring with “difference of squares.”
“Difference of squares” is when the expression you have to factor contains perfect squares. In order for “difference of squares” to work, the numbers have to be perfect squares and you have to be subtracting the constant in your expression.
Expression with all perfect squares:
Step 1: take your expression (or make one) and make sure all given numbers are perfect squares (if they aren’t, then skip to “expression that doesn’t have all perfect squares”)
(ex, using – 4)
Step 2: from here you just have to square each of your numbers and put 2 sets of them in brackets (showing that they are being multiplied)
Step 3: one sign between your variable and constant should be a negative sign and one should be a positive sign because in order to get a negative number you have to multiply a positive and negative
Expression that doesn’t have all perfect squares:
These steps can be used if you have an expression that contains some or no perfect squares.
Step 1: first find the greatest common factor of the numbers in your expression
(ex, using )
Step 2: then you divide all the terms in your expression by the common factors and multiply your entire expression so you aren’t changing the answer.
Step 3: now just put whatever is left inside of brackets and the common factors outside of brackets
Depending on your expression, you could stop here, but if the expression inside of the brackets contains all perfect squares then you can follow the steps for “expression with all perfect squares.”