EDEXCEL GCSE FOUNDATION MATHS - What are Collecting Like Terms

Collecting Like Terms

What are Like Terms?

Like terms are terms that have the same variables raised to the same powers.

Examples of like terms:

• 3x and 5x (both have the variable x to the power of 1)
• 2y^2 and -7y^2 (both have the variable y to the power of 2)
• 4ab and -2ab (both have the variables a and b to the power of 1)

Examples of unlike terms:

• 2x and 3y (different variables)
• 4x^2 and 5x (different powers of x)
• 3ab and 2a (different variables)

Why Collect Like Terms?

Collecting like terms is a fundamental step in simplifying algebraic expressions. It makes it easier to:

• Solve equations
• Factorize expressions
• Understand the relationships between variables

How to Collect Like Terms

1. Identify like terms: Look for terms with the same variables raised to the same powers.

2. Combine coefficients: Add or subtract the coefficients of the like terms.

3. Keep the variables and powers the same: The variables and powers remain unchanged when combining like terms.

Example:

Simplify the expression 3x + 2y - 5x + 4y.

1. Identify like terms:

   • 3x and -5x are like terms.
   • 2y and 4y are like terms.

2. Combine coefficients:

   • 3x - 5x = -2x
   • 2y + 4y = 6y

3. Keep the variables and powers the same:

   • The simplified expression is -2x + 6y.

Practice Problems:

1. Simplify the following expressions:

a) 7a + 2b - 3a + 5b b) 4x^2 - 3x + 2x^2 + 7x c) 5xy - 2x + 3xy + 4x

2. Combine like terms in the following expressions:

a) 2p + 3q - p + 5q b) 6m^2 + 4m - 2m^2 + m c) 8ab - 3a + 5ab + 2a

Answers:

1. a) 4a + 7b b) 6x^2 + 4x c) 8xy + 2x

2. a) p + 8q b) 4m^2 + 5m c) 13ab - a