Question

Factories 36(a+b)^2 -49 ( a-b )^ 2

Answer 1

Answer

36(a+b)^2 -49 ( a-b )^ 2 = (13a - b)(13b -a)

Explanation

36(a+b)^2 -49 ( a-b )^ 2 = [6(a+b)]^2 - [7(a-b)]^2

   =[ 6(a+b) + 7(a-b)][6(a+b) - 7(a-b)]     (because a^2 - b^2 = (a+b)(a-b))

   =(6a + 6b + 7a -7b)(6a + 6b -7a + 7b)

   = (13a - b)(13b -a)

Therefore, 36(a+b)^2 -49 ( a-b )^ 2 = (13a - b)(13b -a)

Answer 2

36(a + b)² - 49(a - b)²

Write each term as a perfect square:

= [ 6(a + b) ]² - [ 7(a - b) ]²

Apply a² - b² = (a + b) (a - b):

= [ 6(a + b) - 7(a - b)] [ 6(a + b) + 7(a - b) ]

Distribute 6 and 7:

= [ 6a + 6b - 7a + 7b] [ 6a + 6b + 7a - 7b]

= [13b - a] [ 13a - b]

Answer: [13b - a] [ 13a - b]