Question

Factorize-16(a+b)²-9(a-b)²​

Answer 1

Solution:

16(a + b)²- 9(a - b)²

= 16(a² + b² + 2ab) - 9(a² + b² - 2ab)

= 16a² + 16b² + 32ab - 9a² - 9b² + 18ab

= 16a² - 9a² + 32ab + 18ab + 16b² - 9b²

= 7a² + 50ab + 7b²

= 7a² + ab + 49ab + 7b²

= a(7a + b) + 7b(7a + b)

= (7a + b) (a + 7b)