What is to use in a binomial? It is to found the difference of squares that we can factor. Such as the formula we use would be perfect square minus a perfect square would let us be able to factor them. Make sure to always check it’s not positive! As that could mess it up, because we want to cancel our sum. 

Now, it would lead us to having conjugates with the example of (x+2)(x-2) = – 4, because it’s all about changing the sign in two terms to get squares. And they must be rational. In this case, we can find that the (a-b)(a+b) would be – .

An important note is to be aware that the perfect square could be hiding in the terms. As you could see, that 3 – 27, which you may think that the 27 could not be any factors besides 9 and 3. That leads you to be writing on 3( – 9), whereas you could do 3(x-3)(x+3) and it would cancel out their sum to match out the expression that is asking you.

Where you could find 4 – 16 that may to be (2x-4)(2x+4). Although, you want to put the two outside of their bracket, which made the second bracket to be (x+2). It’s even better if you can make it look easier, such as 4(x-2)(x+2). You would ask yourself why is it 4? Well what mutiplies to 4? It’s 2 times by 2. It helps you to use the disturbutive property method that was taught in the first unit of class.

When you come across to 4 + 27, you would find that 27 can be multiplied by 9 and 3. Or another factor we could include is 27 and 1, which most students would tend to forget we can do that. In fact, we would find that this expression is considered to be prime, without their conjugates.

What’s to consider to each answer is make sure they are in a prime expression. How would you make that, by simplify for some terms. For example, I have written that this is

Which the constant of two has been moved as the term outside the brackets. Since dividing by two, makes it as 2 times by 2. You would leave it in the brackets, but you would move the other number to be out.

Your mindset could have been tricked that -50 would is not a perfect square.

In there, you could simplify the expression with 2, this lets it put the 2 as the term away of the brackets. Which cause you to have and -25. We can see there’s both of the perfect squares and a negative sign for you to make conjugates out of them. What would you do to have your answer?

It could trick you when there is an expression of 49-4h, you know what’s wrong? The variable is not in their exponent, which meant it is not a perfect square. The exponent must be an even number to be able for you to solve. This 4h is considering to be not factorable, and so this whole thing is a prime.

This topic has taught me so many things about what is able to factor to make my homework more understandable. But it’s not hard to learn about them! Since, you had already known what’s the perfect squares for yourself to solve the questions that are asked.