Algebra Worksheet for 14-Year-Olds: Collecting Like Terms & Simplifying Expressions

Instructions

Read each section carefully. Your goal is to simplify the algebraic expressions by collecting 'like terms'. Like terms are terms that have the same variable(s) raised to the same power. For example, 3x and 5x are like terms, but 3x and 5x² are not. Write your simplified answer in the space provided.

For each question, identify and write down all the terms from the list that are 'like' the bolded term.

1. 6a

   List: 7b, -3a, 6a², 12, a², 10a, -a

   Like Terms: ___________________________



2. -2x²y

   List: -2xy, 10x²y, 4x², 5xy², x²y, -2y²x

   Like Terms: ___________________________

Simplify the following expressions by collecting like terms.

1. 4x + 7x + 2x = _________________
2. 9y + y + 3z + 5z = _________________
3. 8b + 5c + 3b + 4c = _________________
4. 12p + 6q + p + 9q = _________________
5. m + m + n + n + m = _________________

Be careful with the positive and negative signs! Simplify these expressions.

1. 10k - 4k + 5 = _________________
2. 6m - 11m = _________________
3. 9 - 3x + 8x - 2 = _________________
4. 5g - 7h - 3g + 12h = _________________
5. -4y + 5z - y - 8z = _________________

Remember, you can only combine terms if the variable and its exponent are exactly the same.

1. 4x² + 6x + 8x² + 3x = _________________
2. 11y² - 5y² + 4y - 8 = _________________
3. a² + 4ab - 7ab + 5a² = _________________
4. 12c² - c + 6c - 4c² - 3 = _________________
5. x² + 2y² + 7x² - 5y² + 3xy = _________________

Find a simplified expression for the perimeter of the rectangle described below. The perimeter is the total distance around the outside of a shape.

• A rectangle has a length of (5x + 2) and a width of (2x - 1).
• Hint: The formula for the perimeter of a rectangle is 2(length + width).

Simplified Expression for Perimeter: ___________________________

Answer Key

1. -3a, 10a, -a
2. 10x²y, x²y

1. 13x
2. 10y + 8z
3. 11b + 9c
4. 13p + 15q
5. 3m + 2n

1. 6k + 5
2. -5m
3. 5x + 7
4. 2g + 5h
5. -5y - 3z

1. 12x² + 9x
2. 6y² + 4y - 8
3. 6a² - 3ab
4. 8c² + 5c - 3
5. 8x² - 3y² + 3xy

• Perimeter = 2((5x + 2) + (2x - 1))
• = 2(5x + 2x + 2 - 1)
• = 2(7x + 1)
• = 14x + 2