Algebraic expressions use letters (variables) to represent unknown numbers. They're like mathematical sentences that describe relationships.
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)
3x + 2y - 5
3x: coefficient 3, variable x
2y: coefficient 2, variable y
-5: constant term
Like terms have exactly the same variables with the same powers. We can add or subtract like terms.
✓ Like Terms:
3x and 5x
2y² and -4y²
7 and -3 (constants)
✗ Unlike Terms:
3x and 2y
x² and x
5xy and 3x
Step 1: Group like terms
(3x + 5x) + (2y - y) + 4
Step 2: Combine coefficients
8x + y + 4
Answer: 8x + y + 4
When we expand brackets, we multiply everything inside the bracket by what's outside.
3(x + 4) = 3x + 12
-2(3y - 5) = -6y + 10
x(2x + 3) = 2x² + 3x
6x + 9 = 3(2x + 3)
x² + 5x = x(x + 5)
4y² - 8y = 4y(y - 2)
Substitution means replacing variables with specific numbers to find the value of an expression.
Step 1: Substitute the values
3(4) + 2(-1)
Step 2: Calculate
12 + (-2) = 10
1. Simplify: 5x + 3 + 2x - 1
2. Expand: 3(x + 4)
3. Find the value of 2x - y when x = 5 and y = 3