Factorising Non-Monic Quadratic Trinomials: Perfect Squares

Factorising Non-Monic Quadratic Trinomials Perfect Squares
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What I’m going to do? I’m going to start with 4x and 4x. Remember I said I usually like to start with the ones that are closer together. I don’t know I always have a tendency to start with the ones that are closer together because usually, they’re the right answer. So I’ll try 4x and 4x and if that doesn’t work I’ll switch around and try a different one like two and eight.

But I’ll start with this first of all. This one’s easy because it’s just one, so it’s just going to be one and one. Now, look! 4x times 1 is 4x, 4x times 1 is 4x, and together they make 8x which is this one. If you did have 2 and 8, you really can’t make 8 with those numbers, can you? That’s why trying to pick the right number at the very beginning if you can.

So, it’s simply going to be 4x plus 1, 4x plus 1 which is, how do we simplify that guys? 4x plus 1 squared! the perfect square! Because we’ve got two of a kind, okay? Now it’s not x’s we’ve got a is and b is involved but that’s okay we’ll stick to that, that’s all right. 4a squared, I’m going to use 2a and 2a. You could use 4a and 1a but again I just like to use the ones that are closer together.

And then, 9b squared that would be 3b and 3b. I’m assuming this might turn into a perfect square, don’t you think? Let’s try. 2a or sorry 2a and 3b is 6ab, 2a and 3b is also 6ab, so together they make 12ab which is exactly what we’ve got. So, 2a plus 3b, 2a plus 3b. How do we simplify that? So so simple. 2a plus 3b squared, okay? So perfect square again.


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