Algebraic Expressions • Topic 6 of 7

Simplification

Simplifying an expression means writing it in its shortest equivalent form by combining like terms and applying the distributive law. First distribute any factors over brackets, a(b + c) = ab + ac, then group like terms and add their coefficients. Pay close attention to signs, especially when a minus sign sits in front of a bracket: −(x − 3) becomes −x + 3. A simplified expression has no remaining brackets and no two like terms left uncombined. The SAT frequently rewards simplifying before solving, because a tidy expression makes the next step obvious.

✅ Solved examples

1. Simplify 3x + 2x + 5.
Combine like terms 3x + 2x = 5x, giving 5x + 5.
2. Simplify 4(x + 2).
Distribute: 4·x + 4·2 = 4x + 8.
3. Simplify 2(x + 3) + 5x.
Distribute: 2x + 6; add 5x to get 7x + 6.
4. Simplify 7x − (2x − 4).
Distribute the minus: 7x − 2x + 4 = 5x + 4.

✏️ Practice — try these, take hints as needed

1. Simplify 5x + 3x − 2.
Combine like terms 5x + 3x.
8x.
Keep the constant.
8x − 2.
2. Simplify 3(x + 4).
Distribute the 3.
3·x and 3·4.
Combine.
3x + 12.
3. Simplify 2(x + 1) + 3x.
Distribute: 2x + 2.
Add 3x.
Combine like terms.
5x + 2.
4. Simplify 6x − (x − 5).
Distribute the minus sign.
6x − x + 5.
Combine.
5x + 5.
5. Simplify 4(2x − 1) + 3.
Distribute: 8x − 4.
Add 3.
Combine constants.
8x − 1.

📝 Topic test — 8 questions

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