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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
5.5 Revision of Algebraic Expressions - V

Examples:
  1. Expand, (2x + y + 3z)2.
    Given that, (2x + y + 3z)2, this is in the form of (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
    Here a = 2x, b = y and c = 3z.
    = (2x)2 + y2 + (3z)2 + 2.2x.y + 2.y.3z + 2.3z.2x
    = 4x2 + y2 + 9z2 + 4xy + 6yz + 12xz
  2. Expand, 27x3 + y3.
    Given that, 27x3 + y3, We write this as (3x)3 + (y)3,
    this is in the form of a3 + b3 = (a+b)(a2 - ab + b2)
    Here, a = 3x and b = 2y
    = (3x + 2y) ((3x)2 - 3x.2y - (2y)2)
    = (3x + 2y)(9x2 - 6xy + 4y2)
  3. Expand, 8x3 - y3.
    Given that, 8x3 - y3 we can write this as (2x)3 - (y)3.
    This is in the form of a3 - b3 = (a - b)(a2 + ab + b2),
    here, a = 2x, and b = y
    = (2x - y)((2x)2 + 2x.y + y2)
    = (2x - y)(4x2 + 2xy + y2)

Directions: Solve the following problems. Also write at least 10 examples of your own.
Q 1: Expand, 27x3 - 125y3.
(3x - 5y)(9x2 + 15xy + 9y2)
(3x - 5y)(9x2 + 15xy + 25y2)
(3x - 5y)(9x2 + 10xy + 25y2)

Q 2: Expand, 8x3 + 125y3.
(2x + 5y)(4x2 - 15xy + 25y2)
(2x + 5y)(4x2 - 10xy + 25y2)
(2x + 5y)(4x2 - 12xy + 25y2)

Q 3: Expand, (x - y - 3z)2.
x2 + y2 + 9z2 - 2xy - 12xz + 6yz
x2 + y2 + 9z2 - 2xy - 6xz + 6yz
x2 + y2 + 9z2 - 6xy - 6xz + 6yz

Q 4: Expand, (x - 3y + 2z)2.
x2 + 9y2 + 4z2 - 6xy - 6yz + 4xz
x2 + 9y2 + 4z2 - 6xy - 12yz + 4xz
x2 + 9y2 + 4z2 - 4xy - 12yz + 4xz

Q 5: Expand, 8x3 + 27y3.
(2x + 3y)(4x2 - 6xy + 9y2)
(2x + 3y)(4x2 - 8xy + 9y2)
(2x + 3y)(4x2 - 12xy + 9y2)

Q 6: Expand, (x + 2y + 3z)2.
x2 + 4y2 + 9z2 + 4xy + 6xz + 12yz
x2 + 4y2 + 9z2 + 4xy + 6xz + 6yz
x2 + 4y2 + 9z2 + 4xy + 12xz + 12yz

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Question 8: This question is available to subscribers only!


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