Combining Like Terms with Distributive Property

Understanding the Distributive Property

​The distributive property is a powerful tool in math that helps us simplify expressions. It works like this:

a(b+c) = ab + ac

This means when we multiply a number by a sum, we can distribute the multiplication to each term inside the parentheses.

Example: 3(4+2) = 3×4 + 3×2 = 12 + 6 = 183 (4+2) = 3 × 4 + 3 ×2 = 12 + 6 = 18

The distributive property helps us break down complex expressions into simpler parts, making them easier to work with.

• 3x and 3y (different variables)

• 2x and 2^2 (different powers)

• 5xy and 5x (different variables)

​Non-Examples:

• 5x and 3x (both have just x)

• 7y^2 and -2y^2 and (both have y^2)

• 44 and 99 (constants are like terms)

​Examples:

​When we use the distributive property, we often create like terms that can be combined:

Example 1:
2(x + 3) + 5 = 2x + 6 + 5x (using distributive property)
=2x + 5x + 6 (rearranging terms)
=7x + 6 (combining like terms)

​When we use the distributive property, we often create like terms that can be combined:

Example 2:
4(2y + 1) - 3y = 8y + 4 - 3y (using distributive property)
=8y - 3y + 4 (rearranging terms)
=5y + 4 (combining like terms)

​Remember to:

1. Use the distributive property first

2. Identify the terms

3. Combine the terms

4. Write your final simplified expression