Class 8 Standard Identities — practice questions with answers

Algebra · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Which expression is the correct expansion of (a + b)² ?

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Answer: B) a² + 2ab + b²

The standard identity is (a + b)² = a² + 2ab + b².

2. Expand (x + 5)(x - 2) using a standard identity.

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Answer: A) x² + 3x - 10

(x + 5)(x - 2) = x² + (5 + (-2))x + (5)(-2) = x² + 3x - 10.

3. Expand

(x + \frac{1}{2})^{2}

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Answer: A)

x^{2} + x + \frac{1}{4}

(x + \frac{1}{2})^{2} = x^{2} + 2 (x) (\frac{1}{2}) + (\frac{1}{2})^{2} = x^{2} + x + \frac{1}{4}

4. In a quiz, Kabir is asked to find a value of c so that 9x² + 30x + c is a perfect square trinomial.
What value of c should he choose?

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Answer: B) 25

9x² + 30x + c = (3x)² + 2(3x)(5) + 5² needs c = 25, giving (3x + 5)².

5. Priya checks that for any number x, the expression x² - (x - 1)(x + 1) is always the same value.
What is that constant value?

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Answer: C) 1

(x - 1)(x + 1) = x² - 1, so x² - (x² - 1) = 1 for every x. The constant value is 1.

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