By the time math students reach grade 7 they will have studied algebra for a few years now. During this time, it’s likely that the majority of students will accept algebra for what it is: a strange topic in math class that uses letters instead of numbers. As grade 7 algebra begins, even the best math students can end up thinking they may need some extra help with algebra.
One of the many reasons this can be true is that at this age, students begin learning about proofs. Learning how you’re meant to answer a specific question when there are no numbers in the example can be very tricky for students. Throw some factors and powers in there, and it’s no wonder that so many students opt for additional online math tutoring to help them through this difficult class.
However, no matter how difficult some of these math problems appear, they can all be solved, and they can all be solved in a manner that is memorable, engaging, and prepares math students for their next challenge, whether that’s a challenging class curriculum, the all-important SATs, or an upcoming math competition.
One example that we can take a look at today is the difference of two squares. Factoring quadratic equations is a skill that can take some getting used to, but once kids grasp it, it’s another tool to add to their mathematical belt.
Difference of squares pattern
As we know from previous blog articles, polynomials have multiple terms. Here is an example of a polynomial:
X2–4XY+Y
In this example, we have three terms. The x-squared, the xy, and the y. Of course, polynomials can also contain constants, variables, and exponents. As we know, in this first example, 4 is a constant, the 2 in x-squared is an exponent and the x in x-squared, the xy, and y are variables.
Now, let’s get specific with the kind of equation we are interested in, one involving the difference of two squares. To solve these equations, we first need to learn the procedure involved in attacking a question like this. We call this procedure the difference of squares pattern.
a2-b2
(a+b)(a−b)
a2+2ab-2ab-b2
Therefore, (a+b)(a−b) = a2-b2
This identity (a+b)(a−b) = a2-b2 can be used to find every difference of squares. As mentioned, however, there are sometimes more steps to the procedure.
Examples
Now that we know how to solve these problems. Let’s take a look at a few examples using different variables and figures. For this example, let’s also run through the specific steps that need to be taken to solve:
- Write down two brackets.
- We want to find the square root of the first term and write it on the left-hand side of both brackets.
- Then we want the square root of the last term and write it on the right-hand side of both brackets.
- Finally, we put a + in the middle of one bracket and a – in the middle of the other. It doesn’t matter which bracket gets which sign.
x2– 16
(x)2 – (4)2
(x – 4)(x + 4)
There are several other methods of factorizing polynomials, and if you would like to check them out head to this link. Furthermore, if you want to try and get faster and faster at solving these types of equations, you can play around with this calculator that solves similar problems. It can be a great way to practice and begin to answer these tricky algebra problems much faster when the SAT or the next math competition pops up.
Online Math Tutoring For Your Child
With a little help from Online Math Center, your young math learner – and soon-to-be fully-fledged mathemetician – can go beyond learning how to solve equations and score well on tests. They can get a proper understanding of the math topics they are studying, utilizing the techniques gained to take on more challenging problems in the future.
Whether your child is in middle school, or high school, or needs to cram for upcoming SAT exams, or a stacked math competition, we have got the resources, experience, and expert teachers to help them get there. We offer one-to-one tutoring where students can plug any gaps in their knowledge, and we offer comprehensive SAT or math competition prep classes, helping students reach their particular exam goals.
Contact OMC today to sign your child up for future success in math class.
