Simplify two minus two 𝑦 plus four minus seven 𝑦. Circle your answer. The options are negative two minus nine 𝑦, six minus nine 𝑦, six minus five 𝑦, and negative two minus five 𝑦.
So when we’re looking to simplify an expression like this, all we look to do is collect like terms. And when we say collect like terms, we mean terms that have a variable that has the same power. For example, if we just had two numbers, so two add three, we can collect these. It would be equal to five. And if we had three 𝑥 plus four 𝑥, these are like terms that got the same power of 𝑥. So this would be equal to seven 𝑥.
However, we cannot simplify or collect terms that don’t have the same variable. So, for instance, three 𝑥 plus four 𝑦 would remain as three 𝑥 plus four 𝑦 because we’ve got 𝑥 and 𝑦. They’re not the same. Similarly, if we had three 𝑥 squared plus four 𝑥, again we couldn’t combine these or we couldn’t collect these terms because these have a different power of 𝑥. Or even though they’re both 𝑥, one is 𝑥 squared and one is just 𝑥 or 𝑥 to the power of one.
Okay, great, so now that we know that, let’s get on and let’s simplify our expression. So I’m gonna start with our numbers. And what I tend to do to make sure that I don’t make any mistakes is circle the terms that we’re dealing with. So we’ve got two and then we’ve got positive four.
And as you can see, here I’ve got the circle around the sign in front of the four because this is very important because this is a sign that relates to the numbers, in this case four. So we know that it’s positive. So therefore, we know that the start of our simplified expression is going to be six, because two add four is six. Then we have negative two 𝑦 minus seven 𝑦.
And if we think about what negative two 𝑦 minus seven 𝑦 is going to be, let’s look at this number line. So we’ve got negative two. And then we want to subtract seven. It means that we’re gonna be left or down our number line seven spaces. So this will take us to negative nine. So therefore, if we have negative two 𝑦 and we subtract seven 𝑦 away from it, we’re gonna have negative nine 𝑦. So we’re left with six minus nine 𝑦.
So therefore, we can say that, fully simplified, two minus two 𝑦 plus four minus seven 𝑦 is six minus nine 𝑦. And we’ve shown that by circling the second answer.