Expanding Double Brackets
Question 1:
Expand the following double brackets:
1(a) (x + 5)(x - 7)
ANSWER: Multiple Choice (Type 1)
A: x^2 -2x -35
B: x^2 + 2x + 35
C: x^2 -7x -35
D: x^2 +7x +35
Workings: (x + 5)(x - 7) = x^2+5x-7x-35 = x^2 -2x -35
Marks = 1
1(b) (x + 5)(x - 3)
ANSWER: Multiple Choice (Type 1)
A: x^2 +4x -15
B: x^2 -5x -15
C: x^2 -2x +5
D: x^2 +2x -15
Workings: (x + 5)(x - 3) = x^2+5x-3x-15 = x^2 +2x -15
Marks = 1
1(c) (x + 7)(x - 7)
ANSWER: Multiple Choice (Type 1)
A: x^2 -14x+49
B: x^2 -49
C: 7x^2 -7x
D: x^2 + 49
Workings: (x + 7)(x - 7) = x^2 +7x-7x -49
Marks = 1
1(d) (x - 5)(x +6)
ANSWER: Multiple Choice (Type 1)
A: x^2 -2x+11
B: x^2+x-30
C: x^2 -3x +11
D: x^2 + 30
Workings: (x - 5)(x +6) = x^2 -5x + 6x -30 = x^2 +x - 30
Marks = 1
1(e) (x + 8)(x + 1)
ANSWER: Multiple Choice (Type 1)
A: x^2 - 8x + 8
B: x^2+ 9x + 9
C: x^2 + 9x + 8
D: x^2 +7x + 8
Workings: (x + 8)(x + 1) = x^2 + 8x +x + 8
Marks = 1
Question 2:
Expand the following double brackets:
2(a) (2? + 2)(4? − 6)
ANSWER: Multiple Choice (Type 1)
A: 6x^2 -2x -20
B: 4x^2-12x +8
C: 8x^2-4x-12
D: 8x^2 +4x + 12
Workings: (2x + 2)(4x - 6) = 8x^2 -12 x +8x -12 = 8x^2-4x-12
Marks = 1
2(b) (7x-8)(2x+8)
ANSWER: Multiple Choice (Type 1)
A: 14x^2 +x - 64
B: 14x^2 +40x - 64
C: 14x^2 +36x - 54
D: 14x^2 +50x - 64
Workings: (7x-8)(2x+8) = 14x^2 + 56x - 16x - 64 = 14x^2 +40x - 64
Marks = 1
2(c) (8x + 3)(5x - 1)
ANSWER: Multiple Choice (Type 1)
A: 40x^2 +x - 64
B: 40x^2 + 7x -3
C: 40x^2 +36x - 54
D: 40x^2 +50x - 64
Workings: (8x + 3)(5x - 1) = 40x^2 - 8x + 15x -3 = 40x^2 + 7x -3
Marks = 1
2(d) (2x + 3)(7x + 3)
ANSWER: Multiple Choice (Type 1)
A: 14x^2 +x - 64
B: 14x^2 +40x - 64
C: 14x^2 + 27x + 9
D: 14x^2 +50x - 64
Workings: (2x + 3)(7x + 3) = 14x^2 +21x + 6x +9 = 14x^2 + 27x + 9
Marks = 1
2(e) (3x - 1)(6x - 8)
ANSWER: Multiple Choice (Type 1)
A: 18x^2 - 30x + 8
B: 9x^2 - 15x + 8
C: 18x^2 - 24x - 8
D: 9x^2 - 16x - 8
Workings: (3x - 1)(6x - 8) = 18x^2 - 24x - 6x + 8 = 18x^2 - 30x + 8
Marks = 1
Question 3:
Expand the following double brackets:
3(a) (5? − 3)(−4? + 2)
ANSWER: Multiple Choice (Type 1)
A: −20?^2+22?−6
B: −20?^2-22?+12
C: 20?^2- 18x−6
D: 20?^2+ 12?−6
Workings: (5? − 3)(−4? + 2) = -20x^2+12x+10x -6 = −20?^2+22?−6
Marks = 1
3(b) (4? + 4)(−3? + 1)
ANSWER: Multiple Choice (Type 1)
A: -7x^2-8x+5
B: 7x^2-3x+4
C: -12x^2-8x+4
D: 12x^2-5x+3
Workings: −12?^2−12?+4?+4 = -12x^2-8x+4 = -12x^2-8x+4
Marks = 1
3(c) (3? − 2)(−4? − 5)
ANSWER: Multiple Choice (Type 1)
A: −12?^2−7?+10
B: 8?^2−4?+10
C: -8?^2−6?+10
D: 12?^2−2?+10
Workings: (3? − 2)(−4? − 5) = −12?^2+8? −15?+10 = −12?^2−7?+10
Marks = 1
3(d) (−4? − 1)(3? + 7)
ANSWER: Multiple Choice (Type 1)
A: −12?^2−31?−7
B: −7?^2−28x−7
C: −12?^2+31?−7
D: 7?^2−28?−7
Workings: (−4? − 1)(3? + 7) = −12?^2−28?−3?−7 = −12?^2−31?−7
Marks = 1
3(e) (8? − 5)(−? + 8)
ANSWER: Multiple Choice (Type 1)
A: −6?^2+69? −40
B: −8?^2+54? −13
C: −6?^2+54? − 13
D: −8?^2+69? −40
Workings: (8? − 5)(−? + 8) = −8?^2+5?+64? −40 = −8?^2+69? −40
Marks = 1
Question 4:
Expand the following:
4(a) (? + 5)(? − 7)−(?+2)^2
ANSWER: Multiple Choice (Type 1)
A: -5x-24
B: x^2-6x+35
C: −6?−39
D: 2x^2-6x-35
Workings: (? + 5)(? − 7)−(?+2)^2 = ?^2+5?−7?−35−(?^2+4?+4) = −6?−39
Marks = 2
4(b) (? +2)^2+(2?+2)^2
ANSWER: Multiple Choice (Type 1)
A: 5?^2-12?-8
B: 3x^2+12x+5
C: 6?^2+10?+5
D: 5?^2+12?+8
Workings: (? +2)^2+(2?+2)^2 = ?^2+4?+4+4?^2+8?+4 = 5?^2+12?+8
Marks = 2
4(c) (? + 7)^2+(3?−2)(?+1)−?
ANSWER: Multiple Choice (Type 1)
A: 2x^2+12x+42
B: 4x^2+14x+47
C: 2x^2+12x+39
D: 6x^2+14x+49
Workings: (? + 7)^2+(3?−2)(?+1)−? = x^2+14x+49+3x^2+x-2-x = 4x^2+14x+47
Marks = 2
Question 5:
A rectangle is shown below.
Find an expression for area of the rectangle.
ANSWER: Multiple Choice (Type 1)
A: 3x^2 + 4x
B: 2?^2−3
C: 2x^2 + 1
D: 2?^2−2
Workings: (2x+2)(x-1)=2x^2+2x-2x-2 = 2x^2-2
Marks = 2
Question 6:
A triangle is shown below.
Find an expression for area of the triangle.
ANSWER: Multiple Choice (Type 1)
A: 3x^2+12x+10
B: x^2-11x+5
C: x^2+11x+10
D: 2x^2+22x+20
Workings: 1/2 (2x+2)(x+10)=1/2 (2x^2+20x+2x+20) = x^2+11x+10
Marks = 2
Question 7:
A cinema discovers that when tickets are £7, all 220 seats are filled.
Ticket price rises occur in 50p increases.
For every ticket price increase of 50p, 10 fewer people attend a film.
The expression for this is (0.5?+7)(220−10?)
7(a) Expand the brackets for this equation.
ANSWER: Multiple Choice (Type 1)
A: -5x^2+40x+1540
B: -4x^2+30x+1240
C: -5x^2-42x+1240
D: 5x^2-30x+1540
Workings: 110x-5x^2+1540-70x = -5x^2+40x+1540
Marks = 1
7(b) Find out the total earned, if the manager increases the price of the ticket five times.
ANSWER: Multiple Choice (Type 1)
A: £1215
B: £1615
C: £1345
D: £1085
Workings: -5(5)^2+40(5)+1540 = £1615
Marks = 1