Algebra, NAPX-J4-CA21

Question

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Worked Solution

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Variant 0

DifficultyLevel

582

Question

Which expression is equivalent to 12x12\large x + 24?

Worked Solution

Check each option:
3(4x3(4\large x + 8) = (3×4x3 \times 4\large x) + (3 × 8\times\ 8)
= 12x12\large x + 24  ✓\checkmark

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Which expression is equivalent to $12\large x$ + 24?
workedSolution
sm_nogap Check each option:
| | | | ------------- | ---------- | | {{{correctAnswer}}} | \= ($3 \times 4\large x$) + (3 $\times\ 8$) | | |= $12\large x$ + 24  $\checkmark$ |
correctAnswer
$3(4\large x$ + 8)

Answers

Is Correct?Answer
✓

3(4x3(4\large x + 8)

x

3(4x3(4\large x + 21)

x

6(2x6(2\large x + 18)

x

12(x12(\large x + 24)

Variant 1

DifficultyLevel

584

Question

Which expression is equivalent to 24m24\large m −- 16?

Worked Solution

Check each option:
4(6m4(6\large m −- 20) = (4×6m4 \times 6\large m) −- (4 × 20\times\ 20)
= 24m24\large m −- 80  x

4(6m4(6\large m −- 4) = (4×6m4 \times 6\large m) −- (4 × 4\times\ 4)
= 24m24\large m −- 16  ✓\checkmark

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Which expression is equivalent to $24\large m$ $-$ 16?
workedSolution
sm_nogap Check each option:
| | | | ------------- | ---------- | | $4(6\large m$ $-$ 20) | \= ($4 \times 6\large m$) $-$ (4 $\times\ 20$) | | |= $24\large m$ $-$ 80  x |

| | | | ------------- | ---------- | | {{{correctAnswer}}} | \= ($4 \times 6\large m$) $-$ (4 $\times\ 4$) | | |= $24\large m$ $-$ 16  $\checkmark$ |
correctAnswer
$4(6\large m$ $-$ 4)

Answers

Is Correct?Answer
x

4(6m4(6\large m −- 20)

✓

4(6m4(6\large m −- 4)

x

12(2m12(2\large m −- 4)

x

24(m24(\large m −- 2)

Variant 2

DifficultyLevel

586

Question

Which expression is equivalent to 15y15\large y + 25?

Worked Solution

Check each option:
15(y15(\large y + 5) = (15×y15 \times \large y) + (15 × 5\times\ 5)
= 15y15\large y + 75  x

15(y15(\large y + 1) = (15×y15 \times \large y) + (15 × 1\times\ 1)
= 15y15\large y + 15  x

5(3y5(3\large y + 5) = (5×3y5 \times 3\large y) + (5 × 5\times\ 5)
= 15y15\large y + 25  ✓\checkmark

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Which expression is equivalent to $15\large y$ + 25?
workedSolution
sm_nogap Check each option:
| | | | ------------- | ---------- | | $15(\large y$ + 5) | \= ($15 \times \large y$) + (15 $\times\ 5$) | | |= $15\large y$ + 75  x |

| | | | ------------- | ---------- | | $15(\large y$ + 1) | \= ($15 \times \large y$) + (15 $\times\ 1$) | | |= $15\large y$ + 15  x |

| | | | ------------- | ---------- | | {{{correctAnswer}}} | \= ($5 \times 3\large y$) + (5 $\times\ 5$) | | |= $15\large y$ + 25  $\checkmark$ |
correctAnswer
$5(3\large y$ + 5)

Answers

Is Correct?Answer
x

15(y15(\large y + 5)

x

15(y15(\large y + 1)

✓

5(3y5(3\large y + 5)

x

5(3y5(3\large y + 25)

Variant 3

DifficultyLevel

587

Question

Which expression is equivalent to 18y18\large y + 36?

Worked Solution

Check each option
18(y18(\large y + 36) = (18×y18 \times \large y) + (18 × 36\times\ 36)
= 18y18\large y + 648  x

6(6y6(6\large y + 3) = (6×6y6 \times 6\large y) + (6 × 3\times\ 3)
= 36y36\large y + 18  x

3(12y3(12\large y + 12) = (3×12y3 \times 12\large y) + (3 × 12\times\ 12)
= 36y36\large y + 36  x

6(3y6(3\large y + 6) = (6×3y6 \times 3\large y) + (6 × 6\times\ 6)
= 18y18\large y + 36  ✓\checkmark

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Which expression is equivalent to $18\large y$ + 36?
workedSolution
Check each option
| | | | ------------- | ---------- | | $18(\large y$ + 36) | \= ($18 \times \large y$) + (18 $\times\ 36$) | | |= $18\large y$ + 648  x |

| | | | ------------- | ---------- | | $6(6\large y$ + 3) | \= ($6 \times 6\large y$) + (6 $\times\ 3$) | | |= $36\large y$ + 18  x |

| | | | ------------- | ---------- | | $3(12\large y$ + 12) | \= ($3 \times 12\large y$) + (3 $\times\ 12$) | | |= $36\large y$ + 36  x |

| | | | ------------- | ---------- | | {{{correctAnswer}}} | \= ($6 \times 3\large y$) + (6 $\times\ 6$) | | |= $18\large y$ + 36  $\checkmark$ |
correctAnswer
$6(3\large y$ + 6)

Answers

Is Correct?Answer
x

18(y18(\large y + 36)

x

6(6y6(6\large y + 3)

x

3(12y3(12\large y + 12)

✓

6(3y6(3\large y + 6)

Variant 4

DifficultyLevel

585

Question

Which expression is equivalent to 20p20\large p −- 48?

Worked Solution

Check each option:
2(10p2(10\large p −- 24) = (2×10p2 \times 10\large p) −- (2 × 24\times\ 24)
= 20p20\large p −- 48  ✓\checkmark

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Which expression is equivalent to $20\large p$ $-$ 48?
workedSolution
sm_nogap Check each option:
| | | | ------------- | ---------- | | {{{correctAnswer}}} | \= ($2 \times 10\large p$) $-$ (2 $\times\ 24$) | | |= $20\large p$ $-$ 48  $\checkmark$ |
correctAnswer
$2(10\large p$ $-$ 24)

Answers

Is Correct?Answer
✓

2(10p2(10\large p −- 24)

x

6(5p6(5\large p −- 8)

x

8(4p8(4\large p −- 6)

x

5(4p5(4\large p −- 8)

Variant 5

DifficultyLevel

587

Question

Which expression is equivalent to 21m21\large m −- 35?

Worked Solution

Check each option:
3(7m3(7\large m −- 15) = (3×7m3 \times 7\large m) −- (3 × 15\times\ 15)
= 21m21\large m −- 45  x

7(3m7(3\large m −- 5) = (7×3m7 \times 3\large m) −- (7 × 5\times\ 5)
= 21m21\large m −- 35  ✓\checkmark

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Which expression is equivalent to $21\large m$ $-$ 35?
workedSolution
sm_nogap Check each option:
| | | | ------------- | ---------- | | $3(7\large m$ $-$ 15) | \= ($3 \times 7\large m$) $-$ (3 $\times\ 15$) | | |= $21\large m$ $-$ 45  x |

| | | | ------------- | ---------- | | {{{correctAnswer}}} | \= ($7 \times 3\large m$) $-$ (7 $\times\ 5$) | | |= $21\large m$ $-$ 35  $\checkmark$ |
correctAnswer
$7(3\large m$ $-$ 5)

Answers

Is Correct?Answer
x

3(7m3(7\large m −- 15)

✓

7(3m7(3\large m −- 5)

x

7(5m7(5\large m −- 3)

x

21(m21(\large m −- 2)

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