Algebraic Expressions

Algebra • Topic 6 • beginner

🔤 What Are Algebraic Expressions?

Algebraic expressions use letters (variables) to represent unknown numbers. They're like mathematical sentences that describe relationships.

Key Terms

Variable: Letter representing unknown (x, y, a)

Coefficient: Number in front of variable (3x → 3)

Constant: Number without variable (5, -7)

Term: Part separated by + or - (3x, 2y, 5)

Example Expression

3x + 2y - 5

3x: coefficient 3, variable x

2y: coefficient 2, variable y

-5: constant term

🔄 Collecting Like Terms

Like terms have exactly the same variables with the same powers. We can add or subtract like terms.

Like Terms Examples

✓ Like Terms:

3x and 5x

2y² and -4y²

7 and -3 (constants)

✗ Unlike Terms:

3x and 2y

x² and x

5xy and 3x

Step-by-Step: Simplify 3x + 2y + 5x - y + 4

Step 1: Group like terms

(3x + 5x) + (2y - y) + 4

Step 2: Combine coefficients

8x + y + 4

Answer: 8x + y + 4

📏 Expanding Brackets

When we expand brackets, we multiply everything inside the bracket by what's outside.

Single Brackets

3(x + 4) = 3x + 12

-2(3y - 5) = -6y + 10

x(2x + 3) = 2x² + 3x

Factorizing (Reverse)

6x + 9 = 3(2x + 3)

x² + 5x = x(x + 5)

4y² - 8y = 4y(y - 2)

🔢 Substitution

Substitution means replacing variables with specific numbers to find the value of an expression.

Example: Find 3x + 2y when x = 4 and y = -1

Step 1: Substitute the values

3(4) + 2(-1)

Step 2: Calculate

12 + (-2) = 10

🎯 Interactive Practice

1. Simplify: 5x + 3 + 2x - 1

2. Expand: 3(x + 4)

3. Find the value of 2x - y when x = 5 and y = 3