91Ó°ÊÓ

When simplifying algebraic expressions, one important concept is to combine like terms. Like terms are terms that have the same variable raised to the same power. Therefore, the coefficients of these terms can be added or subtracted.

For example, in the expression \(4y - y\), both terms have the variable \(y\). You can combine these like terms by subtracting the coefficients. Here’s how you do it:

1. Identify the like terms. In this case, \(4y\) and \(-y\) are like terms.
2. Combine them by subtracting their coefficients: \(4 - 1 = 3\).

So, \(4y - y = 3y\).

This makes the expression simpler, as combining like terms reduces the number of terms, making it easier to work with.

Simplifying algebraic expressions involves combining like terms and applying arithmetic operations to make the expression as concise as possible. The aim is to rewrite the expression in its simplest form.

Let’s break it down with an example involving the initial expression:

\[ (4y - 1) - (y - 2) \]

Follow these steps for simplification:

1. **Distribute the negative sign** over the terms inside the parentheses (next section explains this in more detail). This changes the expression to:
\[ 4y - 1 - y + 2 \]
2. **Combine like terms** (as explained in the previous section):
\[ 4y - y = 3y \]
3. Combine the constants \(-1 + 2 = 1\)

So, after combining like terms and constants, the simplified form of the initial expression is:
\[ 3y + 1 \]

Simplifying expressions not only makes them easier to handle but also helps in solving potential equations and inequalities faster.

Distributing a negative sign through an expression involves applying the negative sign to each term inside the parentheses. This essentially means multiplying each term by \(-1\).

Consider the initial expression given:

\[ (4y - 1) - (y - 2) \]

When you distribute the negative sign through the second set of parentheses, each term changes as follows:
\[ (y - 2) \rightarrow -y + 2 \]

This turns the original expression into:
\[ 4y - 1 - y + 2 \]

Here’s a step-by-step breakdown:
1. Take each term inside \(y - 2\) and multiply by \(-1\):
\begin{itemize}

\(y \times (-1) = -y\)

\