📚 Part 1: Understanding Algebra Terms

Key Terms:

Variable: A letter that represents an unknown number (e.g., x, y, a)

Coefficient: The number in front of a variable (e.g., in 5x, the coefficient is 5)

Constant: A number on its own with no variable (e.g., 7, -3)

Index (Power): The small number that shows how many times to multiply (e.g., in x², the index is 2)

Like Terms: Terms with the same variable and same power (e.g., 3x and 7x are like terms)

In the expression: 4x + 7

The constant in 3y - 8 is:

In the term 6a², the coefficient is _____, the variable is _____, and the index is _____.

In the expression 2x + 5y - 9, there are _____ terms and the constant is _____.

🔄 Part 2: Collecting Like Terms

Instructions: Like terms have the same variable with the same power. To collect like terms, add or subtract their coefficients.

Example: 3x + 5x = 8x (because 3 + 5 = 8)

Example: 7y - 2y = 5y (because 7 - 2 = 5)

a) 4x + 3x = _____________

b) 7a - 2a = _____________

c) 5y + 2y - y = _____________

d) 3m + 4n + 2m = _____________

e) 8p - 3p + 5 = _____________

f) 2x + 3y + 5x - y = _____________

a) 4a + 3b - 2a + 5b - 1

b) 7x² + 3x - 2x² + 5x

c) 3m + 4n - m + 2n + 6

✖️ Part 3: Multiplying Terms

Instructions: When multiplying terms:

• Multiply the numbers (coefficients) together

• Multiply the variables by adding their indices

Examples: 3 × 4x = 12x, 2x × 5y = 10xy, 3a × 4a = 12a²

a) 3 × 5x = _____________

b) 4 × 2y = _____________

c) 6 × 3a = _____________

d) 2x × 3 = _____________

e) 5y × 4 = _____________

f) 7 × (-2m) = _____________

a) 2a × 3b = _____________

b) 4x × 5y = _____________

c) 3m × 2m = _____________

d) 5p × 4p = _____________

e) 2x × 3x × 4 = _____________

What is 3a × 4a?

➗ Part 4: Dividing Terms

Instructions: When dividing terms:

• Divide the numbers (coefficients)

• Divide the variables by subtracting their indices

Examples: 12x ÷ 3 = 4x, 15a ÷ 5a = 3, 8x² ÷ 2x = 4x

a) 12x ÷ 4 = _____________

b) 20y ÷ 5 = _____________

c) 18a ÷ 6 = _____________

d) 15m ÷ 3m = _____________

e) 24p ÷ 8p = _____________

f) 14x² ÷ 7x = _____________

a) 21a³ ÷ 3a

b) 36x²y ÷ 6xy

c) 45m²n ÷ 9mn

🔀 Part 5: Mixed Practice

a) 3x + 5x - 2x

b) 4a × 3a

c) 18y ÷ 6

d) 2m + 3n + 5m - n

e) 5p × 2 + 3p

f) 12x² ÷ 4x + 2x

🌟 Part 6: Extension Questions

a) Simplify: 3x² + 5x + 2x² - 3x + 7

b) If 4a × 3b = 24ab, find the value when a = 2 and b = 3

c) Simplify: (2x + 3y) + (5x - y) - (x + 2y)

A rectangle has a length of (3x + 2) metres and a width of (2x - 1) metres.

a) Write an expression for the perimeter of the rectangle

b) Simplify your expression

c) If x = 4, what is the actual perimeter in metres?

a) 3x² × 4x³

b) 2a²b × 5ab²

c) (-3m²) × 4mn

Write an algebraic expression with at least 4 terms that can be simplified to 3x + 5: