Expanding & Simplifying Algebraic Expressions — Worksheet & Memo

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Grade 8 · Algebraic Expressions

Expanding & Simplifying Algebraic Expressions

MARKING GUIDELINE

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 31

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
5(x + 2) = …
(1)
A)x + 10
B)5x + 2
C)7x
D)5x + 10✓
Answer: D — The 5 multiplies BOTH terms in the bracket.
- A — multiplied only the second term
- B — multiplied only the first term
- C — added 5 and 2 to x
1.2
3x(x + 5) = …
(1)
A)8x²
B)3x² + 5
C)3x² + 15x✓
D)3x + 15x
Answer: C — 3x × x = 3x² and 3x × 5 = 15x.
- A — added everything together
- B — multiplied only the first term
- D — forgot to multiply the x terms
1.3
−2(x − 4) = …
(1)
A)−2x + 8✓
B)−2x − 8
C)−2x − 4
D)2x − 8
Answer: A — −2 × (−4) = +8: multiplying two negatives gives a positive.
- B — kept the minus on the second term
- C — did not multiply the 4
- D — dropped the minus on the first term
1.4
Simplify: 4(x + 2) − 3x
(1)
A)x + 6
B)x + 8✓
C)x + 2
D)7x + 8
Answer: B — 4x + 8 − 3x = x + 8.
- A — subtracted 2 as well
- C — did not expand the bracket first
- D — ADDED the 3x instead of subtracting it
1.5
−3x(2x − 5 + y) = …
(1)
A)−6x² − 15x − 3xy
B)−6x² + 15x + y
C)−6x² + 15x − 3xy✓
D)−6x + 15x − 3xy
Answer: C — Multiply −3x into EVERY term: −3x × 2x = −6x², −3x × (−5) = +15x and −3x × y = −3xy.
- A — −3x × (−5) is POSITIVE: a negative times a negative
- B — multiplied only the first two terms and left y alone
- D — forgot that x × x = x²
1.6
Divide: 12x³/4x, x ≠ 0
(1)
A)3x²✓
B)3x⁴
C)8x²
D)3x³
Answer: A — 12 ÷ 4 = 3 and x³ ÷ x = x².
- B — added the exponents
- C — subtracted the coefficients
- D — forgot to subtract the exponents
1.7
Determine the value of 4a − b if a = 3 and b = 5.
(1)
A)−7
B)7✓
C)17
D)12
Answer: B — 4(3) − 5 = 12 − 5 = 7.
- A — subtracted the wrong way round
- C — added the 5
- D — forgot to subtract b
1.8
(3x²)² = …
(1)
A)6x⁴
B)3x⁴
C)9x²
D)9x⁴✓
Answer: D — Square the 3 AND the x²: 3² = 9 and (x²)² = x⁴.
- A — doubled the 3 instead of squaring it
- B — squared only the x², not the 3
- C — squared the 3 but left x² as it was
1.9
Simplify: 2(3x − 1) + 3(x + 4)
(1)
A)9x + 10✓
B)9x − 10
C)9x + 3
D)6x + 10
Answer: A — 6x − 2 + 3x + 12 = 9x + 10.
- B — used −12 instead of +12
- C — subtracted 2 from 12 instead of adding
- D — forgot to expand the second bracket
1.10
Which one of the following is EQUAL to 6x + 9?
(1)
A)6(x + 9)
B)3(2x + 9)
C)3(2x + 3)✓
D)3(2x + 6)
Answer: C — The common factor is 3: 3 × 2x = 6x and 3 × 3 = 9.
- A — did not divide the 9 by 6
- B — did not divide the 9 by 3
- D — divided the 9 by 3 but wrote 6

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[9 MARKS]

Expand the following.

2.1
5(x + 2), and hence simplify 5(x + 2) − 3x
(3)
= 5 × x + 5 × 2 (1)
= 5x + 10 (1)
5x + 10 − 3x = 2x + 10 (1)
2.2
3x(x + 5), and hence simplify 3x(x + 5) + 2x²
(3)
= 3x × x + 3x × 5 (1)
= 3x² + 15x (1)
3x² + 15x + 2x² = 5x² + 15x (1)
2.3
−2(y − 4)
(3)
−2 × y = −2y (1)
−2 × (−4) = +8 (1)
= −2y + 8 (1)

Question 3

[12 MARKS]

Expand and simplify the following.

3.1
3(x + 2) + 2(x + 1)
(3)
= 3x + 6 + 2x + 2 (2)
= 5x + 8 (1)
3.2
6 − 3(x − 2)
(3)
= 6 − 3x + 6 (2) — note −3 × (−2) = +6
= 12 − 3x (1)
3.3
Simplify: (10x² + 5x) ÷ 5x, x ≠ 0
(3)
Divide EACH term by 5x (1)
= 10x²/5x + 5x/5x (1)
= 2x + 1 (1)
3.4
Determine the value of 5a − b if a = 4 and b = 7, and then its value if a = 4 and b = −7.
(3)
5(4) − 7 = 13 (1)
5(4) − (−7) = 20 + 7 (1)
= 27 — subtracting a negative ADDS (1)

TOTAL: 31 marks

This question paper consists of 3 questions.