How to Simplify Algebraic Expressions

Simplifying algebraic expressions might seem tricky at first, but it gets easier with practice. Let's go through it step by step!

Step 1: Understand the Expression

Before we start simplifying, it's important to know what the expression looks like.

Take a look at its parts:

• Constants: These are numbers.
• Variables: These are letters like $x$ or $y$ that represent unknown values.
• Operations: These include addition, subtraction, multiplication, and division.

For example, in the expression $3x + 4 - 2x$, we can see two terms with the variable $x$.

Step 2: Combine Like Terms

Now, let's find the like terms. These are terms that have the same variable and power.

In our example, $3x$ and $-2x$ are like terms. To simplify them, we can combine them:

$$3x - 2x = 1x = x$$

So, the expression $3x + 4 - 2x$ becomes $x + 4$.

Step 3: Distribute When Necessary

If you see a term being multiplied by parentheses, you’ll need to distribute that term to all parts inside the parentheses.

For example, in the expression $2(x + 3)$, you need to multiply $2$ by both $x$ and $3$:

$$2(x + 3) = 2x + 6$$

Be careful with distribution to avoid mistakes!

Step 4: Factor When Possible

Sometimes, you can simplify even more by factoring.

For example, in the expression $2x + 4$, we can factor out $2$:

$$2x + 4 = 2(x + 2)$$

Factoring helps make equations easier to solve.

Step 5: Use the Order of Operations

Remember the order of operations. A handy way to remember it is with the acronym BIDMAS/BODMAS, which stands for:

• Brackets
• Indices
• Division and Multiplication
• Addition and Subtraction

This will help you solve more complicated expressions.

For example, when simplifying $3 + 2(4 - 1)$, do the operation in the brackets first:

$$4 - 1 = 3$$

Then, do the multiplication:

$$2 \times 3 = 6$$

Finally, add:

$$3 + 6 = 9$$

Step 6: Double-Check Your Work

After you think you’ve simplified the expression, take a moment to review each step. Make sure you didn’t make any mistakes or skip any terms.

Practice Makes Perfect!

The more you practice these steps, the easier it will get. Try working on different expressions, and soon you’ll be simplifying like a pro!