Like terms are really important when we want to make algebraic problems easier to solve.

So, what are like terms? They are terms that have the same variable and the same exponent (or power). For example, $3x$ and $5x$ are like terms because they both have the variable $x$. The same goes for $2y^2$ and $4y^2$—they both have the variable $y$, raised to the second power.

To simplify an expression, we first need to find these like terms. Once we spot them, we can combine them by either adding or subtracting their numbers (which we call coefficients).

Let’s say we have the expression $3x + 5x$.

We can see that both terms have the variable $x$. To simplify this, we just add the numbers together:

$$3x + 5x = (3 + 5)x = 8x.$$

This way, we make the expression cleaner, and we also end up with fewer terms. This helps us do our calculations more easily.

Another reason like terms are handy is that they help us compare and change expressions without a lot of hassle. For example, in the expression $2y^2 - 3y^2 + 4y$, we can only combine $2y^2$ and $-3y^2$ because they are like terms. When we do the math, we get:

$$2y^2 - 3y^2 = -1y^2 = -y^2,$$

so now we have $-y^2 + 4y$ left.

Finally, using like terms makes solving equations easier. It cuts down on confusion and helps us focus on isolating the variables we want to solve for.

In short, like terms help us work with algebraic expressions better. They make math clearer and quicker to handle!