Simplifying Expressions

🧹 Simplifying Expressions

What Does "Simplify" Mean?

To simplify an expression means to rewrite it in the shortest, cleanest way possible — without changing its value. A simplified expression is easier to read and easier to use later.

We simplify by:

• Combining like terms
• Using the distributive property
• Removing parentheses
• Writing in standard form (variables first, then the number)

Example:

Both expressions are equal — they give the same answer for any value of $x$ — but the simplified version is much cleaner.

🔑 Key Idea: Simplifying never changes what the expression equals. It only changes how it looks.

🧩 Like Terms

Like terms have the same variable raised to the same power. Only like terms can be combined.

✅ Like Terms (can combine)

• $3x$ and $5x$ — both have $x$
• $-2y$ and $7y$ — both have

➕ Combining Like Terms

To combine like terms, add or subtract the coefficients (the numbers in front) and keep the variable part the same.

Example: $4x + 7x$

• Both terms have $x$.
• Add the coefficients: $4 + 7 = 11$.
• Keep the variable: .

✅ Concept Check

📝 Worked Examples: Grouping Like Terms

When an expression has a mix of variable terms and constants, the trick is to group the like terms first, then combine each group.

Example 1 — Variables and constants

Simplify $3x + 7 + 2x - 4$.

• Step 1 — Group like terms.
  • $x$ terms: $$

🎯 Guided Practice: Combine Like Terms

Add or subtract the coefficients in the order they appear, and keep each term's sign.

🔽 Choose the Simplified Form

Pick the correct simplified expression for each one.

🌍 The Distributive Property in Real Life

Sometimes an expression has parentheses. To remove them, use the distributive property:

$a(b + c) = ab + ac$

Multiply the number outside the parentheses by each term inside.

Example: $3(x + 4)$

🏆 Review: Simplifying Expressions

You can now shrink messy expressions into clean ones using like terms and the distributive property. Here's the big picture: