Multiplication and Standard Identities Quiz - CBSE Class 8 Mathematics

Free practice quiz: Multiplication and Standard Identities (CBSE Class 8 Mathematics). 14 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. Expand (x + 3)(x - 3)

   1. x² - 9
   2. x² + 9
   3. x² + 6x - 9
   4. x² - 6x + 9
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   Answer: A. x² - 9

   This is a difference of squares. (a + b)(a - b) = a² - b². Therefore, (x + 3)(x - 3) = x² - 3² = x² - 9.

2. Find the value of (99)² using a suitable identity.

   1. 9801
   2. 9901
   3. 10000
   4. 9701
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   Answer: A. 9801

   We can write 99 as (100 - 1). Then (99)² = (100 - 1)² = 100² - 2(100)(1) + 1² = 10000 - 200 + 1 = 9801. This uses the identity (a - b)² = a² - 2ab + b².

3. Simplify (x + y)(x - y) + (x + y)²

   1. 2x² + 2xy
   2. 2x² + 2xy + 2y²
   3. 2x²
   4. 2x² + 2y²
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   Answer: A. 2x² + 2xy

   Expand each part: (x + y)(x - y) = x² - y² and (x + y)² = x² + 2xy + y². Adding them, we get x² - y² + x² + 2xy + y² = 2x² + 2xy.

4. If a + b + c = 0, prove that a³ + b³ + c³ = 3abc

   1. True
   2. False
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   Answer: A. True

   This is a standard identity. Start with the identity a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca). If a + b + c = 0, the right side becomes 0, implying a³ + b³ + c³ = 3abc.

5. Simplify (a+b)(a-b) - (a-b)^2

   1. 2b(a-b)
   2. 2a(a-b)
   3. 2a(a+b)
   4. 2b(a+b)
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   Answer: A. 2b(a-b)

   First expand: (a+b)(a-b) = a^2 - b^2 and (a-b)^2 = a^2 - 2ab + b^2. Subtracting the second from the first gives (a^2 - b^2) - (a^2 - 2ab + b^2) = 2ab - 2b^2 = 2b(a-b)

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