Expanding Triple Brackets
Question 1:
Fully expand and simplify (x+ 2)(x+3)(x+4)
ANSWER: Multiple Choice (Type 1)
A: ?^3-6?^2-26?+20
B: ?^3+9?^2+26?+24
C: 3?^3-6?^2+26?+24
D: 2?^3+9?^2+20?+20
Workings: (x^2+5x+6)(x+4) = x^3+5?^2+6?+4?^2+20?+24 =?^3+9?^2+26?+24
Marks = 3
Question 2:
Fully expand and simplify (m-1)(m+2)(m+5)
ANSWER: Multiple Choice (Type 1)
A: 3m^3+9m^2+3m -10
B: m^3+6m^2+3m -10
C: m^3+9m^2+6m -7
D: 2?^3+6?^2+3? +7
Workings: (m^2+m-2)(m+5) = m^3+m^2-2m+5m^2+5m -10 =m^3+6m^2+3m -10
Marks = 3
Question 3:
Fully expand and simplify (y-2)(y-6)(y-2)
ANSWER: Multiple Choice (Type 1)
A: 3y^3-20y^2+20y -24
B: 2y^3-9y^2+24y -21
C: y^3-5y^2+14y -21
D: y^3-10y^2+28y -24
Workings: y^2−8?+12)(y−2) =y^3-8y^2+12y - 2y^2+16y-24 =y^3-10y^2+28y -24
Marks = 3
Question 4:
Fully expand and simplify (3x+5)(x+1)(4+x)
ANSWER: Multiple Choice (Type 1)
A: 2x^3+10x^2-37x-20
B: 3x^3+25x^2+37x+25
C: 3x^3+20x^2+37x+20
D: x^3+20x^2+34x-20
Workings: (3x^2+8x+5)(4+x) = 12x^2+32x+20+3x^3+8x^2+5x =3x^3+20x^2+37x+20
Marks = 3
Question 5:
Fully expand and simplify -(2x-3)(x+5)(y+3)
ANSWER: Multiple Choice (Type 1)
A: -2x^2 y-7xy+15y-6x^2-21x+45
B: -2x^2 y-2xy+5y-16x^2-25x+45
C: -3x^2 y-7xy+5y-6x^2-21x+5
D: -3x^2 y-7xy-15y-6x^2-21x+5
Workings: -((2x^2+7x-15)(y+3)) = -(2x^2 y+7xy-15y+6x^2+21x-45) = -2x^2 y-7xy+15y-6x^2-21x+45
Marks = 3
Question 6:
A triangular prism is shown below.
The base of the face is 2x-2.
The height of the face is x+3.
The length of the prism is 2x+4.
Find an expression, in terms of x, for the volume of the triangular prism.
ANSWER: Multiple Choice (Type 1)
A: -2x^2 y-7xy+15y-6x^2-21x+45
B: -2x^2 y-2xy+5y-16x^2-25x+45
C: -3x^2 y-7xy+5y-6x^2-21x+5
D: -3x^2 y-7xy-15y-6x^2-21x+5
Workings:
Area of face= \frac{1}{2}(2x-2)(x+3) = \frac{1}{2}(2x^2+4x-6) = x^2+2x-3Volume of prism=(x^2+2x-3)(2x+4) =2x^3+4x^2-6x+4x^2+8x -12 = 2x^3+8x^2+2x -12
Marks = 5