Distribute, Then Collect
Part of the Expressions & Data section of Coddy's Pre-Algebra journey. Lesson 20 of 52.
Some expressions need both skills. 3(x + 4) + 2x has like terms hiding inside parentheses. First expand: 3 times x is 3x and 3 times 4 is 12, giving 3x + 12 + 2x. Now the like terms are in the open, and 3x + 2x is 5x, so the result is 5x + 12.
The order matters. The 3 multiplies the whole bracket, so you cannot add it to the 2x first: 3(x + 4) is not three plus anything. Parentheses go first, exactly as in the order of operations, and collecting comes after.
Write one step per line: expand, then collect. If the expansion line is wrong, the board refuses it before you build on it.
Challenge
Simplify 2(x + 3) + 5x. Expand on your first line, then combine the like terms.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Expressions & Data
1Variables and Expressions
What a Variable IsWriting ExpressionsExpressions from StoriesTwo OperationsRecap: Expressions4Combining Like Terms
Like TermsLetters and NumbersNegative TermsTwo LettersDistribute, Then CollectRecap: Like Terms2Evaluating Expressions
Substituting a ValueNegative InputsPowers in ExpressionsFormulasRecap: Evaluating5Patterns and Sequences
Continuing a PatternThe Common DifferenceThe nth TermWriting the RuleRecap: Sequences3The Distributive Property
Number PropertiesMental MathDistributing LettersDistributing a MinusRecap: Distributing