Seventh Grade · Math · week 19

Simplifying expressions with distribution

Simplify linear expressions with rational coefficients by distributing over parentheses and combining like terms.

An expression is fully simplified once every parenthesis has been distributed away and every like term has been combined into one. Distributing means multiplying the number outside a parenthesis by EVERY term inside it, including a negative sign out front.

After distributing, gather like terms (terms with the exact same variable part) and combine them by adding or subtracting their coefficients. The order you do this in never changes the final simplified expression.

📋 For the teacher
Teach it (10–15 min):
  • Have them draw an arrow from the outside number to EACH term inside the parentheses -- it prevents distributing to only the first term.
  • Watch negative distribution closely: -3(x - 4) becomes -3x + 12, not -3x - 12 -- the sign of the second term flips too.
  • Only combine terms that have the exact same variable part; a plain number and an x-term can never combine.
  • Practice the reverse direction too: factoring an expression back into a number times a parenthesis.
Talk about it:
  • Why does distributing require multiplying EVERY term inside the parentheses, not just the first one?
  • What happens to the sign of the second term when you distribute a negative number?
  • How do you know which terms in an expression are allowed to combine?

Mastery looks like: They distribute across parentheses (including negative multipliers) and combine like terms into a fully simplified expression.

Common stumbles: Distributing to only the first term inside the parentheses; forgetting that a negative multiplier flips the sign of every term inside.

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