Find the expansion of the following using a suitable identity.
(i) (3x + 7y) (3x - 7y)
(ii) (4x/5 + y/4) (4x/5 + 3y/4)

Solution:

(i) (3x + 7y) (3x - 7y)

Using the identity (a + b) (a - b) = a² - b²,

Substitute a = 3x and b = 7y,

(3x + 7y) (3x - 7y) = (3x)² - (7y)²

= 9x² - 49y²

(ii) (4x/5 + y/4) (4x/5 + 3y/4)

Using the identity (x + a) (x + b) = x² + (a + b)x + ab,

substitute x = 4x/5, a = y/4 and b = 3y/4

(4x/5 + y/4) (4x/5 + 3y/4) = (4x/5)² + [(y/4 +3y/4)4x/5] + [(y/4)(3y/4)]

= (16x²/25) + [(4y/4)4x/5] + (3y²/16)

= (16x²/25) + (16xy/20) + (3y²/16)

= (16x²/25) + (4xy/5) + (3y²/16)

✦ Try This: Find the expansion of the following using a suitable identity. (2a + 3b) (2a - 3b)

Given, (2a + 3b) (2a - 3b)

Using the identity (x + y) (x - y) = x² -y²,

Substitute x = 2a and y = 3b ,

(2a + 3b) (2a - 3b) = (2a)² - (3b)²

= 4a² - 9b²

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

NCERT Exemplar Class 8 Maths Chapter 7 Sample Problem 11

Summary:

The expansion of (i) (3x + 7y) (3x - 7y) (ii) (4x/5 + y/4) (4x/5 + 3y/4) are 9x² - 49y² and (16x²/25) + (4xy/5) + (3y²/16) respectively

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