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
Solution:
Given (1) (21x + 13y)²
Using standard identity: (a + b)² = a² + 2ab + b²
(21x + 13y)² = (21x)² + 2(21x)(13y) + (13y)²
= 441x² + 546xy + 169y² ⇒ option (b) of column II
(2) (21x - 13y)²
Using standard identity: (a - b)² = a² - 2ab + b²
(21x - 13y)² = (21x)² - 2(21x)(13y) + (13y)²
= 441x² - 546xy + 169y² ⇒ option (c) of column II
(3) (21x - 13y) (21x + 13y)
Using standard identity: (a - b)(a + b) = a² - b²
(21x - 13y) (21x + 13y) = (21x)² - (13y)²
= 441x² - 169y² ⇒ option (a) of column II
✦ Try This: Match the expressions of column I with that of column II:
COLUMN I COLUMN II
(i) (13x + 14y)² (a) 169x² - 196y²
(ii) (13x - 14y)² (b) 169x² + 364 xy - 196y²
(iii) (13x + 14y)(13x - 14y) (c) 169x² - 364 xy + 196y²
(d) 169x² + 364 xy+ 196y²
(i) (13x + 14y)²
Using standard identity: (a + b)² = a² + 2ab + b²
(13x + 14y)² = (13x)² + 2(13x)(14y) + (14y)²
=169x² + 364 xy + 196y²⇒ option (d) of column II
(ii) (13 x - 14y)²
Using standard identity: (a - b)² = a² - 2ab + b²
(13x - 14y)² = (13x)² - 2(13x)(14y) + (14y)²
= 169x² - 364 xy + 196y² ⇒ option (c) of column II
(iii) (13x + 14y)(13x - 14y)
Using standard identity: (a - b)(a + b) = a² - b²
(13x + 14y)(13x - 14y) = (13x)² - (14y)²
=169x² - 196y² ⇒ option (a) of column II
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9
NCERT Exemplar Class 8 Maths Chapter 7 Problem 125
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
Summary:
The matches of column I and II are:
(1) (21x + 13y)² → (b) 441x² + 546xy + 169y²
(2) (21x - 13y)² → ( c) 441x² - 546xy + 169y²
(3) (21x - 13y) (21x + 13y) → (a) 441x² - 169y²
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