Which of the following is an identity?
(a) (p + q)² = p² + q²
(b) p² - q² = (p - q)²
(c) p² - q² = p² + 2pq - q²
(d) (p + q)² = p² + 2pq + q²

Solution:

The correct answer is (d).

Consider (p + q)² = (p + q)(p+q)

= p(p + q) + q(p + q)

= p² + pq + qp + q²

= p² + 2pq + q²

Thus the right identity is (p + q)² = p² + 2pq + q²

✦ Try This: Which of the following is not a true identity? (a) p² - q² = (p + q)(p - q), (b) p³ - q³ = (p - q) (p² + pq + q²), (c) (p + q)² = p² + 2pq + q², (d) (p - q)² = p² + 2pq + q²

By recalling all the identities we can say (d) is the wrong identity.

(p - q)² = (p - q) (p - q)

= p(p - q) - q(p - q)

= p² - pq - qp + q²

= p² - 2pq + q²

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

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NCERT Exemplar Class 8 Maths Chapter 7 Sample Problem 2

Which of the following is an identity? (a) (p + q)² = p² + q², (b) p² - q² = (p - q)², (c) p² - q² = p² + 2pq - q², (d) (p + q)² = p² + 2pq + q²

Summary:

Given (a) (p + q)² = p² + q² (b) p² - q² = (p - q)² (c) p² - q² = p² + 2pq - q² (d) (p + q)² = p² + 2pq + q² , (d) is the correct answer

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