Simplify two multiplied by three 𝑥 plus five minus 𝑥. Circle your answer. The options are five 𝑥 plus five, 15𝑥 , five 𝑥 plus 10, and 10 𝑥.
So to simplify this expression, the first thing we need to do is expand the
bracket. And when we say expand the bracket, what this means is multiply the term or number
outside the bracket by each of the terms inside the bracket.
So first of all, we have two multiplied by three 𝑥. This is gonna give us six 𝑥. And that’s because two multiplied by three is six. And then we’ve got the 𝑥. What I’ve done here is drawn an orange line just to show the multiplication. This can sometimes be a good idea so that you know you haven’t missed anything
Then next, what we have is two multiplied by positive five, which gonna give us
positive 10. So we’ve got six 𝑥 plus 10 and then minus 𝑥. So now have we simplified? Well, we’ve done one step. But we’re not fully simplified yet because now what we can do is collect like
terms. And we know that we’ve got some like terms because I’ve circled them here in
pink. And we know that because these two terms have the same power of 𝑥 in them.
So we have 𝑥 or 𝑥 to the power of one in each of these terms. If we had 𝑥 squared or anything like that, then we wouldn’t be able to add or
subtract them, because we can only do that if they are of the same power. So what we have is six 𝑥 minus 𝑥.
Well, when we’ve just got 𝑥 written, it’s the same as one 𝑥. So we have six 𝑥s minus an 𝑥, which gonna leave us with five 𝑥. And then we have plus 10. So therefore, we can say that if we simplify two multiplied by three 𝑥 plus five
minus 𝑥, the answer will be five 𝑥 plus 10. So we’ve circled this as it’s our third answer.