Simplify variable expressions involving like terms and the distributive property
Simplifying expressions means making them shorter and easier to work with. You do this by combining like terms and using the distributive property.
Concept
**Like Terms:** Terms that have the same variable raised to the same power. * **Like terms:** 3x and 5x, -2y and y, 4 and -10 * **Not like terms:** 3x and 3y, 2x and 2x² **Combining Like Terms:** Add or subtract the coefficients (the numbers in front of the variables). * 3x + 5x = 8x * 7y - 2y = 5y **The Distributive Property:** a(b + c) = ab + ac * 3(x + 2) = 3x + 6 * -2(y - 5) = -2y + 10 **Example:** Simplify 3(x + 2) + 4x - 5 1. **Distribute:** 3x + 6 + 4x - 5 2. **Combine like terms:** (3x + 4x) + (6 - 5) = 7x + 1
Try it
Practice: Simplify variable expressions involving like terms and the distributive property.