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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
5.6 Revision of Algebraic Expressions - VI

Examples:
  1. Expand, (x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3xz).
    Given that, (x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3xz),
    This is in the form of, (a + b + c)(a2 + b2 + c2 - ab - bc - ca) = a3 + b3 + c3 - 3abc.
    Here a = x, b = 2y and c = 3z.
    = (x)3 + (2y)3 + (3z)3 - 3.x.2y.3z
    = x3 + 8y3 + 27z3 - 18xyz
  2. Expand, (7x + 3)(4x+2).
    Given that, (7x + 3)(4x+2).
    This is in the form of (ax + b)(cx + d) = (ac)x2 + (ad + bc)x + bd
    Here a = 7, b = 3, c = 4 and d = 2.
    = (7 * 4)x2 + (7*2 + 4*3)x + 6
    = 28x2 + 26x + 6
  3. Expand, (x+3)(x+2)(x+1).
    Given that, (x+3)(x+2)(x+1).
    Formula for this is , (x+a)(x+b)(x+c) = x3 + (a+b+c)x2 + (ab + bc + ca)x + abc
    Here, a = 3, b = 2 and c = 1
    = x3 + (a+b+c)x2 + (6+2+3)x + 3.2.1
    = x3 + 6x2 + 11x + 6

Directions: Solve the following problems. Also write at least 10 examples of your own.
Q 1: Expand, (2x - 3)(2x + 1).
4x2 - 4x - 3
4x2 - 6x - 3
4x2 - 4x + 3

Q 2: Expand, (2x - 1)(x - 2).
2x2 - 5x + 4
2x2 - 6x + 2
2x2 - 5x + 2

Q 3: Expand, (x + 5)(x + 3)(x + 7).
x3 + 15x2 + 71x + 105
x3 + 15x2 + 71x + 85
x3 + 15x2 + 57x + 105

Q 4: Expand, (x + 3)(x + 1)(x + 4).
x3 + 4x2 + 19x + 12
x3 + 8x2 + 19x + 6
x3 + 8x2 + 19x + 12

Q 5: Expand, (2x + y + z)(4x2 + y2 + z2 - 4xy - yz - 2xz).
8x3 + y3 + z3 - 6xyz
4x3 + y3 + z3 - 3xyz
8x3 + y3 + z3 - 6xyz

Q 6: Expand, (x+y+z)(x2 + y2+z2 - xy - yz - zx).
x3 + y + z3 - 6xyz
x3 + y + 2z3 - 3xyz
x3 + y + z3 - 3xyz

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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