Question

Evaluate (4a+3b)^2- (4a-3b)^2+48ab

Answer 1

(4a+3b)² - (4a-3b)² + 48ab = ((4a+3b) + (4a-3b) ((4a+3b) - (4a-3b) + 48ab 
= (8a) (6b) + 48ab 
= 48ab + 48ab 
= 96ab

Answer 2

Given : (4a+3b)² - (4a-3b)² + 48ab

To find : Evaluate  (4a+3b)² - (4a-3b)² + 48ab

Solution:

(4a+3b)² - (4a-3b)² + 48ab

using

(x + y)² = x² + y² + 2xy

& (x - y)² = x² + y² - 2xy

x = 4a

y = 3b

= (4a)²+ (3b)² + 2(4a)(3b) - ( (4a)²+ (3b)² - 2(4a)(3b))  + 48ab

= 24ab  + 24ab + 48ab

= 96ab

=> (4a+3b)² - (4a-3b)² + 48ab = 96ab

another method

use x² - y² = (x + y)(x - y)

x = 4a + 3b  & y = 4a - 3b

= (4a + 3b + 4a - 3b)(4a + 3b - 4a + 3b) + 48ab

= (8a)(6b) + 48ab

= 48ab + 48ab

= 96ab

(4a+3b)² - (4a-3b)² + 48ab = 96ab

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