Expanding & Simplifying Algebraic Expressions — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

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)5x + 2
B)5x + 10✓
C)x + 10
D)7x
Answer: B — The 5 multiplies BOTH terms in the bracket.
- A — multiplied only the first term
- C — multiplied only the second term
- D — added 5 and 2 to x
1.2
3x(x + 5) = …
(1)
A)3x² + 5
B)3x² + 15x✓
C)3x + 15x
D)8x²
Answer: B — 3x × x = 3x² and 3x × 5 = 15x.
- A — multiplied only the first term
- C — forgot to multiply the x terms
- D — added everything together
1.3
−2(x − 4) = …
(1)
A)−2x − 8
B)−2x + 8✓
C)2x − 8
D)−2x − 4
Answer: B — −2 × (−4) = +8: multiplying two negatives gives a positive.
- A — kept the minus on the second term
- C — dropped the minus on the first term
- D — did not multiply the 4
1.4
Simplify: 4(x + 2) − 3x
(1)
A)x + 8✓
B)7x + 8
C)x + 2
D)x + 6
Answer: A — 4x + 8 − 3x = x + 8.
- B — ADDED the 3x instead of subtracting it
- C — did not expand the bracket first
- D — subtracted 2 as well
1.5
(x + 3)(x + 2) = …
(1)
A)x² + 6
B)x² + 5x + 6✓
C)x² + 6x + 5
D)2x + 5
Answer: B — x² + 2x + 3x + 6.
- A — multiplied only the first and last terms
- C — swapped the middle term and the constant
- D — added instead of multiplying
1.6
Divide: 12x³4x
(1)
A)3x³
B)3x²✓
C)8x²
D)3x⁴
Answer: B — 12 ÷ 4 = 3 and x³ ÷ x = x².
- A — forgot to subtract the exponents
- C — subtracted the coefficients
- D — added the exponents
1.7
Determine the value of 4a − b if a = 3 and b = 5.
(1)
A)17
B)7✓
C)−7
D)12
Answer: B — 4(3) − 5 = 12 − 5 = 7.
- A — added the 5
- C — subtracted the wrong way round
- D — forgot to subtract b
1.8
(x + 4)² = …
(1)
A)x² + 16
B)x² + 8x + 16✓
C)x² + 4x + 16
D)2x + 8
Answer: B — (x + 4)(x + 4) also gives a MIDDLE term of 2 × 4 × x.
- A — squared each term separately — the middle term is missing
- C — used 4x instead of 8x
- D — doubled instead of squaring
1.9
Simplify: 2(3x − 1) + 3(x + 4)
(1)
A)9x + 3
B)9x + 10✓
C)6x + 10
D)9x − 10
Answer: B — 6x − 2 + 3x + 12 = 9x + 10.
- A — subtracted 2 from 12 instead of adding
- C — forgot to expand the second bracket
- D — used −12 instead of +12
1.10
Which one of the following is EQUAL to 6x + 9?
(1)
A)3(2x + 9)
B)3(2x + 3)✓
C)6(x + 9)
D)3(2x + 6)
Answer: B — The common factor is 3: 3 × 2x = 6x and 3 × 3 = 9.
- A — did not divide the 9 by 3
- C — did not divide the 9 by 6
- 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
(3)
Divide EACH term by 5x (1)
= 10x²5x + 5x5x (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.