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