Lesson 6.15Simplify Algebraic Expressions
Set B · Version ASecond form · supported practice
Learning target I can simplify algebraic expressions by combining like terms.
Why This Matters The music studio is placing supply orders for three rehearsal rooms. Room A needs 4 microphones and 3 stands. Room B needs 2 microphones and 5 stands. Room C needs 6 microphones and 1 stand. Instead of ordering separately, you can combine: (4 + 2 + 6) microphones and (3 + 5 + 1) stands = 12 microphones and 9 stands. That's simplifying by combining like items!
RememberSimplify Algebraic Expressions
Combining Like Terms Like terms are terms with the same variable raised to the same exponent, like 2x and 5x. To simplify an expression, you add or subtract the like terms to make it shorter.
- Like Terms: Terms that share the exact same variable part and exponent (e.g. 4x and 2x).
- Add or subtract the coefficients of like terms; keep the variable unchanged.
- Constants (numbers without variables) combine together separately
Words: Like Terms (Términos semejantes)Combine (Combinar)Simplify (Simplificar)Coefficient (Coeficiente)Term (Término)
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1Circle the letter of the best answer. Show how you know.
A music festival needs supplies for 3 stages. Stage 1 needs 8m + 5 cables, Stage 2 needs 3m + 7 cables, and Stage 3 needs 4m + 2 cables, where m represents the number of microphones per stage. The total order is (8m + 5) + (3m + 7) + (4m + 2). What does the 15m tell the festival?
- A15 cables are needed for every microphone
- BThere are 15 microphones
- C15 stages need cables
- DThe cables cost $15
Show your work
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2Circle the letter of the best answer. Show how you know.
Expand 5(x + 3).
- A5x + 15
- B5x + 3
- C8x
- Dx + 15
Show your work -
3Circle the letter of the best answer. Show how you know.
Which shows 6n + 18 factored using its GREATEST common factor?
- A2(3n + 9)
- B3(2n + 6)
- C6(n + 3)
- D6(n + 18)
Show your work -
4Circle the letter of the best answer. Show how you know.
Expand 4(2y − 5).
- A2y − 20
- B6y − 20
- C8y − 20
- D8y − 5
Show your work -
5Circle the letter of the best answer. Show how you know.
Use the distributive property to compute 7 × 62 mentally: 7 × (60 + 2) = ?
- A62
- B420
- C427
- D434
Show each partial product, then add them- 1SplitBreak one factor apart.
- 2MultiplyOne part at a time.
- 3AddAdd the parts.
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6Circle the letter of the best answer. Show how you know.
A music festival needs supplies for 3 stages. Stage 1 needs 8m + 5 cables, Stage 2 needs 3m + 7 cables, and Stage 3 needs 4m + 2 cables, where m represents the number of microphones per stage. The total order is (8m + 5) + (3m + 7) + (4m + 2). Simplify (8m + 5) + (3m + 7) + (4m + 2).
- A12m + 17
- B15m + 14
- C15m + 15
- D29m
Show your work
Explain your thinkingWhat rule determines whether two terms are 'like terms'? Why can't you combine unlike terms?
Sentence starter Two terms are like terms when they have the same ___. You cannot combine ___ and ___ because they represent different ___.
Lesson 6.15Simplify Algebraic Expressions
Set B · Version BSecond form · core practice
Learning target I can simplify algebraic expressions by combining like terms.
Why This Matters The music studio is placing supply orders for three rehearsal rooms. Room A needs 4 microphones and 3 stands. Room B needs 2 microphones and 5 stands. Room C needs 6 microphones and 1 stand. Instead of ordering separately, you can combine: (4 + 2 + 6) microphones and (3 + 5 + 1) stands = 12 microphones and 9 stands. That's simplifying by combining like items!
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1Write the name of the correct group on each line.
The terms are scattered across the mixing board. Sort each term into its like-term group so you know what can be combined.
- 3x
- 5x
- 2x
- 7
- 4
- 9
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2Circle the letter of the best answer. Show how you know.
A music festival needs supplies for 3 stages. Stage 1 needs 8m + 5 cables, Stage 2 needs 3m + 7 cables, and Stage 3 needs 4m + 2 cables, where m represents the number of microphones per stage. The total order is (8m + 5) + (3m + 7) + (4m + 2). If each stage has 4 microphones (m = 4), how many cables in total?
- A29
- B60
- C64
- D74
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3Circle the letter of the best answer. Show how you know.
The board shows 3x + 5x on one channel. Simplify it.
- A8x
- B8x²
- C15x
- D35x
Show your work -
4Circle the letter of the best answer. Show how you know.
Simplify the track: 4a + 2 + a.
- A5a + 2
- B5a²+ 2
- C6a
- D7a
Show your work -
5Circle the letter of the best answer. Show how you know.
Clean up this channel: 7y − 3y.
- A4y
- B4
- C10y
- D21y
Show your work -
6Circle the letter of the best answer. Show how you know.
Simplify the mix: 6m + 4 + 3m.
- A9m + 4
- B9m + 4m
- C10m
- D13m
Show your work