Combining Like Terms

Expressions often contain like terms – terms with the same variable part raised to the same power. Combining them (adding or subtracting their coefficients) simplifies expressions and makes solving equations more efficient. This step is essential before moving terms across the equals sign or factoring.

Imagine simplifying 3x + 5x – 2 + 7. You group the x terms together (3x + 5x) and the constants together (–2 + 7). This reduces clutter and reveals the underlying structure you’ll work with in equations or further manipulations.

Example: Simplify 3x + 5x – 2 + 7.

1. Combine x terms: 3x + 5x = 8x
2. Combine constants: –2 + 7 = 5
3. Write final: 8x + 5.

Hints and tips

• List like terms in columns: Write all x_² terms in one column, all x terms in another, constants in a third – then combine vertically.
• Watch signs carefully: A “−3x + 5x” becomes “+2x” – misreading a minus sign is the most common slip.
• Simplify before expanding further: Combine like terms first to keep your expressions as small as possible when you expand more brackets.
• Check for hidden like terms: After expanding, always scan for newly created like terms you might have overlooked.
• Use color-coding: Highlight each group of like terms in the same color to see at a glance what belongs together.