This week in math we learned how to determine the difference of a square. First, to understand how this works you’ll need to know how conjugates work. A conjugate is when two simple binomials are multiplied together and the answer you get is also a binomial, compared to where you would usually get a trinomial as an answer. This is because the binomials have a zero pair, which cancels out so you are left with a binomial instead of a trinomial. For example: (x-5)(x+5)= x²-25
If you are only given the answer and not the factored form there are some rules as to how you can determine if it’s a conjugate or not. It should be a binomial, second term is negative, x² is in the equation, and it is a perfect square. So say I was given x²-25 instead of the factored form, I could figure out it’s factored form the square-rooting everything in the equation so, we would end up with (x-5)(x+5) as the factored form. That is because the x² = x by x and the square root of 25 is 5 x 5. Since it’s a conjugate, we know that one of the 5’s is positive and one is negative so they create a zero pair.
Know that some questions will not be factorable, for example, If the second term is positive or if it’s not a perfect square then it’s not factorable. You should also see if you can take the GCF (greatest common factor) from the equation. If all parts of the equation (constant, variable, coefficient) can go into a number or/also a variable then you put the GCF in front of the brackets and divide all the numbers in the equation by the GCF then factor the equation. It can make the numbers a lot smaller and easier to work with, so always check if there’s a GCF first!
