Simplifying expressions drills

Combine like terms and apply the distributive property.

Free, timed SHSAT practice sets on simplifying expressions— every question includes a full worked explanation, and there's no account required.

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How to simplify algebraic expressions

Simplify in two steps:

  1. Distribute any number in front of parentheses to every term inside.
  2. Combine like terms: add the \(x\)-terms together and the plain numbers together. Each term keeps the sign in front of it.

Example: \(3(x - 7) - x - 6 = 3x - 21 - x - 6 = 2x - 27\).

To factor, go the other way: divide every term by the common factor. \(12x + 18 = 6(2x + 3)\). Distribute to check: \(6 \cdot 2x = 12x\) and \(6 \cdot 3 = 18\).

Common traps:

Worked examples

Example 1.
Simplify: \(5x + 4 - 8x - 3\).
Show answer and explanation
Answer:
B

Combine the \(x\)-terms: \(5x - 8x = -3x\). Combine the constants: \(4 - 3 = 1\). Result: \(-3x + 1\). (Flipping the sign of \(- 8x\) gives \(13x + 1\). Flipping the sign of \(- 3\) gives \(-3x + 7\). Adding the numbers into the \(x\)-term, as if they were like terms, gives \(-2x\).)

Example 2.
Simplify: \(2(x - 2) + 5x + 7\).
Show answer and explanation
Answer:
D

Distribute: \(2(x - 2) = 2x - 4\). Combine with \(+ 5x + 7\): \(x\)-terms give \(7x\), constants give \(3\). Result: \(7x + 3\). (Multiplying only the \(x\) by \(2\) gives \(7x + 5\). Writing \(+ 4\) instead of \(- 4\) gives \(7x + 11\). Leaving out the \(+ 5x\) term gives \(2x + 3\).)

Example 3.
Which expression is equivalent to \(15x + 24\)?
Show answer and explanation
Answer:
D

Both terms share the factor \(3\): \(15x = 3 \cdot 5x\) and \(24 = 3 \cdot (8)\). So the expression equals \(3(5x + 8)\). Check by distributing: \(3 \cdot 5x = 15x\) and \(3 \cdot (8) = 24\). (Dividing only the \(x\)-term by \(3\) gives \(3(5x + 24)\). Dividing only the constant by \(3\) gives \(3(15x + 8)\). Taking out the whole coefficient \(15\), which does not divide \(24\), gives \(15(x + 8)\).)