Simplifying Algebraic Expressions

Simplifying Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and mathematical operations. Simplifying an algebraic expression means rewriting it in a shorter and clearer form without changing its value.

Simplifying helps make mathematical problems easier to understand and solve.

What Is an Algebraic Expression?

An algebraic expression may contain:

* Variables (such as x or y)

* Numbers (constants)

* Operations (addition, subtraction, multiplication, division)

Example:

3x + 5x

Both terms contain the variable x, so they are called like terms.

Combining Like Terms

Like terms can be combined by adding or subtracting their coefficients.

Example:

3x + 5x

Step 1: Add the coefficients

3 + 5 = 8

Step 2: Keep the variable

Result:

8x

So the simplified expression is:

8x

Example 2

Simplify the expression:

4x + 3 + 2x

Step 1: Identify like terms

4x and 2x are like terms.

Step 2: Add the coefficients

4x + 2x = 6x

Step 3: Write the constant

Final expression:

6x + 3

Example 3

Simplify:

7y − 2y + 5

Step 1: Combine the like terms

7y − 2y = 5y

Step 2: Write the constant

Result:

5y + 5

Quick Tip

Only like terms can be combined.

For example:

3x + 2y cannot be simplified because the variables are different.

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