Simplify four 𝑦 minus two 𝑦 plus 𝑦.
To simplify an algebraic expression like the one we have here means that we need to collect like terms. Like terms are the terms which have the same letters and powers. For example, two 𝑦 and three 𝑦 squared are not like terms as although they have the same letters, they have different powers. The first term just has 𝑦, which is 𝑦 to the power of one, and the second term has 𝑦 squared.
In our expression, all of the terms are actually like terms as they all have the same letter 𝑦 and they all have the same power, which although it isn’t written, is a power of one. To simplify then, we just need to look at how many 𝑦s we have and how many we’re adding or subtracting.
The first part of the expression is four 𝑦 minus two 𝑦. And if you have four of something and then subtract two of the same thing, you’re left with two of them. So four 𝑦 minus two 𝑦 simplifies to two 𝑦. And therefore, the whole expression simplifies to two 𝑦 plus 𝑦.
Now, remember 𝑦 is just a shorthand way of writing one 𝑦. We never write one 𝑦 in algebra. We just write it as 𝑦. So this means two 𝑦 plus one 𝑦. And as two plus one is equal to three, this simplifies to three 𝑦.
The expression four 𝑦 minus two 𝑦 plus 𝑦 simplifies to three 𝑦.