Question

factorise 4x^2 + 9y^2 - 25z^2 +12xy

Answer 1

4x² + 9y² - 25z² + 12xy
⇒ (2x)² + (3y)² - (5z)² + 2.(2x)(3y)
⇒{(2x)² + (3y)² + 2(2x)(3y)} - (5z)²
⇒(2x + 3y)² - (5z)² [ as we know (a + b)² = a² + b² + 2ab ]

use now, (a² - b²) = (a - b)(a + b)
⇒{(2x + 3y) - 5z}{(2x + 3y) + 5z}
⇒(2x + 3y - 5z)(2x + 3y + 5z)

Hence , answer is (2x + 3y - 5z)(2x + 3y + 5z)

Answer 2

Given:
4x² + 9y^² - 25z² +12xy
4x² + 9y² + 12xy - 25z²
(2x)² + (3y)² + 2(2x)(3y) - (5z)²
{(2x)² + (3y)² + 2(2x)(3y)} - (5z)²
(2x + 3y)² - (5z)²
[By using the identity (a + b)² = a² + b² + 2ab ]
{(2x + 3y) - 5z}{(2x + 3y) + 5z}
[By using the identity(a² - b²) = (a - b)(a + b) ]
(2x + 3y - 5z)(2x + 3y + 5z)

HOPE THIS WILL HELP YOU...