Expanding Single Brackets
Question 1:
Expand the following:
1(a) 2(e-8)
ANSWER: Simple Text Answer
2e-16
Workings: 2(e-8)= (2\times e)-(2 \times 8) = 2e - 16
Marks = 1
1(b) 4(c-6)
ANSWER: Simple Text Answer
4c-24
Workings: 4(c-6) = (4\times c)- (4\times 6) = 4c -24
Marks = 1
1(c) 4(d+7)
ANSWER: Simple Text Answer
4d+28
Workings: 4(d+7) = (4\times d)+ (4\times 7) = 4d +28
Marks = 1
1(d) 6(t+7)
ANSWER: Simple Text Answer
6t + 42
Workings: 6(t+7) = (6\times t)+ (t\times 7) = 6t + 42
Marks = 1
1(e) 2(3p-8)
ANSWER: Simple Text Answer
6p - 16
Workings: 2(3p-8) = (2\times 3p) - (2\times 8 ) = 6p -16
Marks = 1
Question 2:
Expand the following:
2(a) 2p(p-9)
ANSWER: Multiple Choice (Type 1)
A: 2p^2 -18p
B: 2p-18p
C: 2p^2-18
D: 2p-9p
Workings: 2p(p-9) = 2p^2 -18p
Marks = 1
2(b) 6a(a+4)
ANSWER: Multiple Choice (Type 1)
A: 7a^2+10a
B: 6a^2+24
C: 6a^2+10a
D: 6a^2+24a
Workings: 6a(a+4) = (6a \times a) + (6a \times 4)
Marks = 1
2(c) 5h(3h-2)
ANSWER: Multiple Choice (Type 1)
A: 2h^2+3h
B: 15h^2-10
C: 15h^2-10h
D: 8h^2-10h
Workings: 5h(3h-2) = (5h\times 3h) - (5h \times 2 )
Marks = 1
2(d) 2e(2e+9)
ANSWER: Multiple Choice (Type 1)
A: 4e^2+18e
B: 4e^2 + 11e
C: 4e +18e
D: 4e^2 +18
Workings: 2e(2e+9) = (2e\times 2e) - (2e \times 9)
Marks = 1
2(e) 2p(5p-4)
ANSWER: Multiple Choice (Type 1)
A: 10p-8
B: 10p^2-8p
C: 7p^2-8p
D: 7p^2-6p
Workings: 2p(5p-4) = (2p\times 5p) - (2p \times 4)
Marks = 1
Question 3:
Which of the following is an expanded form of:
3(a) 5(3a-8)
ANSWER: Multiple Choice (Type 1)
A: 15a-13
B: 8a-3
C: 15a-40
D: 25a
Workings: 5(3a-8) = 15a-40
Marks = 1
3(b) 5x(3x +10y)
ANSWER: Multiple Choice (Type 1)
A: 8x^2 + 50xy
B: 15x^2 + 50xy
C: 15x^2 + 50xy
D: 15x^2 + 50xy
Workings: 5x(3x +10y) = (5x \times 3x) + (5x \times 10y)
Marks = 1
3(c) 8?(3?² + 3?)
ANSWER: Multiple Choice (Type 1)
A: 24?^3
B: ?^2 (?+24)
C: 24?^2+24
D: 24?^2+24?^3
Workings: 8?(3?² + 3?) = 24?^2+24?^3
Marks = 1
3(d) xy(?+4)
ANSWER: Multiple Choice (Type 1)
A: ?^2−2??−24
B: ?^2y+4xy
C: ?^2−24
D: yx^2^2−10?−24
Workings: xy(?+4) = x^2y + 4xy
Marks = 1
Question 4
Which of the following is the expanded form of:
4(a) ?(? + 5) + ?(? + 7)
ANSWER: Multiple Choice (Type 1)
A: 2m^2 + 35
B: 2m^2+12m
C: 2m^2 +12
D: m+12
Workings: ?(? + 5) + ?(? + 7) = 2m^2+12m
Marks = 1
4(b) ?(? + 5) + ?(? + 7)
ANSWER: Multiple Choice (Type 1)
A: 2m^2 + 35
B: 2m^2+12m
C: 2m^2 +12
D: m+12
Workings: ?(? + 5) + ?(? + 7) = 2m^2+12m
Marks = 1
4(c) 4a^3(7ab-8b^2)
ANSWER: Multiple Choice (Type 1)
A: 11?^4 ?−4?^3 ?^2
B: 28?^4 ?^4−32?^3 ?^5
C: 28?^4 ?−32?^3 ?^2
D: 28?^3 ?−32?^3 ?^2
Workings: 4a^3(7ab-8b^2) = 28?^4 ?−32?^3 ?^2
Marks = 1
4(d) 4x(3x - x²) -2x²(4 -5x)
ANSWER: Multiple Choice (Type 1)
A: 4x^2+6x^3
B: 12?^2−4?^3
C: 2?+8?^2
D: 3?(?+2)
Workings: 4x(3x - x²) -2x²(4 -5x) = 12x^2-4x^3 - 8x^2 +10x^3
Marks = 1
Question 5:
Expand and simplify the following expressions:
5(a) 5(3?−7)+3(?+2)
ANSWER: Multiple Choice (Type 1)
A: 18x -29
B: 15x +29
C: 21?+8?
D: 3?+2
Workings: 5(3?−7)+3(?+2) = (15x - 35) + (3x +6)
Marks = 2
5(b) (2y+3)-y(2y-3)
ANSWER: Multiple Choice (Type 1)
A: y^2 +3y
B: 5y + 5
C: y^2
D: 6y
Workings: (2y+3)-y(2y-3)= 2y + 3 -2y^2 +3y
Marks = 2
5(c) 7?(8?−3)−2?(?+10)
ANSWER: Multiple Choice (Type 1)
A: 54?^2−41?
B: 54?−41
C: 54?^2−1?
D: 56?^2+?
Workings: 7?(8?−3)−2?(?+10) = (2y+3)-y(2y-3) = 56?^2−21?−2?^2−20? = 54?^2−41?<br />
Marks = 2
Question 6:
Expand and simplify the following expression
6xy(2x-4)-4(5x^2 y-8xy)
ANSWER: Multiple Choice (Type 1)
A: 28xy-8y
B: 8xy-8x^2
C: 18x-8x^2 y
D: 8y-18x^2 y
Workings: 6xy(2x-4)-4(5x^2 y-8xy) = 12x^2 y-24xy-20x^2 y+32xy = 8xy-8x^2 y
Marks = 2
Question 7:
Mr Jenkins walks ? km to work each day.
Mr Taylor cycles twice as far as Mr Jenkins and then an additional 5 ?? more to get to work.
They both return home after making the same journey back.
7(a) Write the expression, in the form a(??+5), for how far Mr Taylor cycles each day.
2(2x+5)
ANSWER: Multiple Choice (Type 1)
A: x(2x+5)
B: 2(2x+5)
C: (x+10)
D: 5(2x + 1)
Workings: 2(2x+5)
Marks = 2
7(b) Expand the expression for Mr Taylor.
ANSWER: Multiple Choice (Type 1)
A: 4x^2+10
B: 12x+5
C: 4x+10
D: 2x+10
Workings: 4x+10
Marks = 1