Part a) Simplify six 𝑦 plus 𝑦 minus five 𝑦. Part b) Simplify three 𝑥 multiplied by four 𝑥.
If we’re looking at part a, to simplify six 𝑦 plus 𝑦 minus five 𝑦, what we need to
do is collect like terms. And in this expression, all the terms are actually like. And the reason they’re like is because they actually all contain a 𝑦. But more importantly, they all contain a single pair of 𝑦. Because if these were different pairs of 𝑦, then we couldn’t add and subtract them
as we’re about to do.
Well, I’m actually going to simplify this in two steps. First of all, I’m going to add six 𝑦 to 𝑦. But when we see just 𝑦, what it actually means is one 𝑦. It’s just that in the notation that we use in mathematics, we don’t actually write
the one. So we’ve got six 𝑦 plus one 𝑦. But what this actually means is six times 𝑦 plus one times 𝑦. So therefore, this is going to be six 𝑦 — so 𝑦 plus 𝑦 plus 𝑦 plus 𝑦 plus 𝑦 plus
𝑦 — then plus a single 𝑦, so plus another 𝑦, which is going to give us seven
𝑦. And then, we’ve got our minus five 𝑦.
Okay, great so that was the first step because it makes it a bit easier if we deal
with six 𝑦 plus 𝑦 first. So now, we’ve got seven 𝑦 take away five 𝑦 and this would just give us our final
answer which is two 𝑦. And that’s because if you got seven 𝑦s and you subtract five away, you’re left with
two. So we can say that if we simplify six 𝑦 plus 𝑦 minus five 𝑦, the answer is two
Okay, now, let’s move on to part b. So when we’re actually simplifying three 𝑥 multiplied by four 𝑥, so we’re
multiplying two terms. A good thing to do is actually to separate it; it makes it easier to understand. So first of all, we’re actually going to multiply the numbers. So we have three multiplied by four.
And then, we’re going to multiply our 𝑥 terms. So we have 𝑥 multiplied by 𝑥. It’s worth mentioning at this point that when you’ve got a question like this, be
careful with the actual notation. So try and use curly 𝑥s so you can actually distinguish between the 𝑥s and the
multiply sign. You may sometimes see the multiply sign uses a dot in situations like this.
So first of all, we’re going to have 12 and this is because three multiplied by four
is 12. And then, we’re gonna have this multiplied by 𝑥 squared because 𝑥 multiplied by 𝑥
is 𝑥 squared because anything multiplied by itself is that number or that term
But we’ve got 12 multiplied by 𝑥 squared. Have we finished? Well, actually, we’ve done all the simplification. It’s just we need to write it in the correct notation. And when we’re writing algebra, we don’t write 12 multiplied by our 𝑥 term. We would actually write it like this, as 12 𝑥 squared.
So therefore, we can say that three 𝑥 multiplied by four 𝑥 simplifies to 12 𝑥