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Special Algebraic Identities Obtained through Expanding

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6.3Special Algebraic Identities Obtained through Expanding

Special Algebraic Identities Obtained through Expanding Revision Questions

1. . What is the expanded form of

(1 - 3x)2
  1. 1 - 9x
  2. 1 - 9x2
  3. 1 - 6x + 9x2
  4. 1 - 6x + 3x2

Correct Answer: C

2. . What is the value of m if

(2x + 3m)2 = 4x2 + 48x + 144
  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer: D

3. . When expanded, the value of expression

(2x - k)∙(2x + k)
becomes
  1. 2x - k2
  2. 2x2 - k2
  3. 4x2 - k2
  4. 4x2 + k2

Correct Answer: C

4. . Which of the following identities is FALSE?

  1. x2 + y2 = (x + y)2
  2. x3 - y3 = (x - y) · (x - y)2
  3. x3 - y3 = (x - y)3
  4. x2 - y2 = (x + y) · (x - y)

Correct Answer: D

5. . What is the simplest form of the expression

1 - (x - 1)2 - 2x
  1. x2
  2. -x2
  3. -x2 - 4x
  4. -4x + 2

Correct Answer: B

6. . What is the simplest form of the expression

8 -(x + 2)(x2 - 2x + 4) + x ∙ (x - 2)(x + 2)
  1. -4x
  2. -16
  3. x3 - 4x - 16
  4. -x3 - x2 + 4

Correct Answer: A

7. . The algebraic expression

x3 - 3x2 + 3x - 5
is equivalent to
  1. (x - 3)3
  2. (x - 1)3 - 4
  3. (x + 1)(x2 - 4x + 4)
  4. (x + 1)3 - 4

Correct Answer: B

8. . Three friends decide to invest their money in a business which returns double after a certain period. How much more do they earn in total if they invest the money together instead of investing separately? The investment of each friend in terms of a constant m is: Friend 1 = 4m; Friend 2 = 3m; Friend 3 = 5m.

  1. 94m2 more
  2. 54m2 more
  3. 30m2 more
  4. 24m2 more

Correct Answer: A

9. . What is the simplest form of the expression

(2x + 3y + 1)2 - 12xy - 6y
  1. 4x2 + 9y2 + 1
  2. 4x2 + 9y2 + 4x + 1
  3. 4x2 + 9y2 + 4x
  4. 2x2 + 9y2 + 4x

Correct Answer: B

10. . If a2 + b2 = 31 and a - b = 3, then what is a · b?

  1. 28
  2. 25
  3. 22
  4. 11

Correct Answer: D

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