Learning Goal: Use the distributive property and combine like terms to write equivalent expressions.
Vocabulary
like termsTerms with the same variable raised to the same power, like 3x and 5x.
distributive propertyA rule that says a(b + c) = ab + ac; multiply the outside number by each term inside.
combine like termsAdd or subtract the coefficients of like terms to simplify, like 3x + 5x = 8x.
equivalent expressionsTwo expressions that always have the same value for every value of the variable.
What You Need to Know
Distribute by multiplying the outside factor by EVERY term inside the parentheses.
Example: 3(x + 4) = 3·x + 3·4 = 3x + 12.
Only combine like terms: 3x + 5x = 8x, but 3x + 5 cannot be combined.
Constants combine with constants; variable terms combine with matching variable terms.
A variable with no number in front has a coefficient of 1: x = 1x.
You can check equivalence by substituting a number for the variable in both expressions.
Worked Example I Do — watch how it works
Simplify 4(x + 2) + 3x.
Step 1. Distribute the 4: 4·x + 4·2 = 4x + 8.
Step 2. Rewrite the expression: 4x + 8 + 3x.
Step 3. Combine like terms 4x and 3x: 7x + 8.
Answer: 7x + 8
Guided Practice We Do — try it together
1. Use the distributive property to expand 5(n + 3).
💡 Hint: Multiply 5 by n and by 3.
2. Combine like terms: 6y + 2 + 3y.
💡 Hint: Add the coefficients of the y-terms; the 2 stays separate.
3. Simplify 2(a + 4) + a.
💡 Hint: Distribute first, then combine the a-terms.
Independent Practice You Do — show your work
1. Expand 3(x + 6).
2. Combine like terms: 8m + 5m.
3. Simplify 4y + 7 + 2y + 1.
4. Expand 6(2k + 1).
5. Simplify 5(p + 2) + 3p.
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.EE.A.3.
Item 1Selected Response6.EE.A.3
Which expression is equivalent to 3(x + 5)?
Select the correct answer.
Item 2Selected Response6.EE.A.3
Simplify 7a + 4 + 2a.
Select the correct answer.
Item 3Constructed Response6.EE.A.3
A garden has 2 rows of (p + 3) plants and 4 more plants added. Write the total as a simplified expression.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
3x + 18
Independent 2
13m
Independent 3
6y + 8
Independent 4
12k + 6
Independent 5
8p + 10
Item 1 · 6.EE.A.3
C — Distribute the 3 to both terms: 3·x + 3·5 = 3x + 15.
Item 2 · 6.EE.A.3
A — Combine like terms 7a and 2a to get 9a; the constant 4 stays, giving 9a + 4.