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Question
Match the expressions of column I with that of column II:
| Column I | Column II |
| (1) (21x + 13y)2 | (a) 441x2 – 169y2 |
| (2) (21x – 13y)2 | (b) 441x2 + 169y2 + 546xy |
| (3) (21x – 13y)(21x + 13y) | (c) 441x2 + 169y2 – 546xy |
| (d) 441x2 – 169y2 + 546xy |
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Solution
| Column I | Column II |
| (1) (21x + 13y)2 | (b) 441x2 + 169y2 + 546xy |
| (2) (21x – 13y)2 | (c) 441x2 + 169y2 – 546xy |
| (3) (21x – 13y)(21x + 13y) | (a) 441x2 – 169y2 |
Explanation:
(1) We have,
(21x + 13y)2 = (21x)2 + (13y)2 + 2 × 21x × 13y ...[Using the identity, (a + b)2 = a2 + b2 + 2ab]
= 441x2 + 169y2 + 546xy
(2) We have,
(21x – 13y)2 = (21x)2 + (13y)2 – 2 × 21x × 13y ...[Using the identity, (a – b)2 = a2 + b2 – 2ab]
= 441x2 + 169y2 – 546xy
(3) We have,
(21x – 13y)(21x + 13y) = (21x)2 – (13y)2 ...[Using the identity, (a – b)(a + b) = a2 – b2]
= 441x2 – 169y2
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