Lesson 6.146.14 · Part II
Start hereWords, worked example, and sentence starters
Learning target I can use the distributive property to expand and factor expressions.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| The Distributive PropertySpanish: La propiedad distributiva | Multiply a factor by every term inside parentheses. | 3(x + 4) = 3x + 12 |
| Distributive PropertySpanish: Propiedad distributiva | Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac. | 3(4 + 5) = 3×4 + 3×5 = 12 + 15 = 27 — the 3 gets 'distributed' to both the 4 and the 5 |
| FactorSpanish: Factor | A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4. | In 3(x + 2), the 3 is the factor outside the parentheses that multiplies each term inside |
| ExpandSpanish: Desarrollar | To multiply out the parentheses in an expression. | Expand 2(n + 6): multiply 2 × n = 2n and 2 × 6 = 12, so 2(n + 6) = 2n + 12 |
| EquivalentSpanish: Equivalente | Expressions that always have the same value. | 3(x + 4) and 3x + 12 always give the same answer: when x = 2, both = 18; when x = 10, both = 42 |
| CoefficientSpanish: Coeficiente | The number in front of a letter, like the 3 in 3x. | In 6x + 15, the coefficient of x is 6 — it came from distributing in 3(2x + 5) |
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
Word bank The Distributive PropertyDistributive PropertyFactorExpandEquivalentCoefficient
Watch outA common mistake
The most common mistake in The Distributive Property is multiplying the outside factor by only the FIRST term inside the parentheses and forgetting the second — for example, writing 3(x + 4) = 3x + 4 instead of 3x + 12. Before you submit, check: did the outside number reach BOTH terms inside the parentheses?
Lesson 6.146.14 · Part II
Apply Day · Version ASupported practice
Learning target I can use the distributive property to expand and factor expressions.
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1Complete each step, then write the final answer.
Use the distributive property to find 2(10 + 5).
Show your workHint Write 2 × 10 + 2 × 5. Then multiply and add.
Final answer: -
2Complete each step, then write the final answer.
Expand 2(x + 9). Fill in the blank: 2x + ___.
Show your workHint The 2 multiplies the x and the 9. What is 2 × 9?
Final answer: -
3Complete each step, then write the final answer.
Use the distributive property to find 3(20 + 1).
Show your workHint Write 3 × 20 + 3 × 1. Then multiply and add.
Final answer:
Lesson 6.146.14 · Part II
Apply Day · Version BCore practice
Learning target I can use the distributive property to expand and factor expressions.
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1Complete each step, then write the final answer.
Ray says 3(9 + 5) = 3 × 9 + 5, so the value is 32. What mistake did he make? What is the correct value?
Show your workFinal answer: -
2Complete each step, then write the final answer.
Expand 4(3x + 5). Fill in the blank: 12x + ___.
Show your workFinal answer: -
3Complete each step, then write the final answer.
Use the distributive property to find 7(10 + 3).
Show your workFinal answer:
Lesson 6.146.14 · Part II
Apply Day · ChallengeExtension
Learning target I can use the distributive property to expand and factor expressions.
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1Circle the letter of the best answer. Show how you know.
Which expression is equivalent to 6(2x + 5)?
- A2x + 30
- B12x + 30
- C12x + 5
- D12x + 11
Show your work
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2Complete each step, then write the final answer.
Find the missing number so the expressions are equivalent: 4(x + ___) = 4x + 36.
Show your workFinal answer: -
3Complete each step, then write the final answer.
Factor 14x + 21 using the GCF. What number goes outside the parentheses?
Show your workFinal answer: