Question

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

Answer 1

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Answer 2

Solution :

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Given :

To factorize :

4x² + 9y² -25z² + 12xy

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We know that,.

(a + b)² = a² + 2ab + b²

&

a² - b² = (a + b)(a - b)

Hence,

⇒ 4x² + 9y² - 25z² + 12xy

⇒ 4x² + 12xy + 9y² - 25z²

⇒ (2x)² + 2(2x)(3y) + (3y)²  - 25z²

⇒ (2x + 3y)² - 25z²              ∴ (a + b)² = a² + 2ab + b²

⇒ (2x + 3y)² - (5z)²

⇒ [(2x + 3y) + 5z] [(2x + 3y) - 5z]   ∴ a² - b² = (a + b)(a - b)

⇒ (2x + 3y + 5z)(2x + 3y - 5z)

Hence,

4x² + 9y² - 25z² + 12xy  = (2x + 3y + 5z)(2x + 3y - 5z)

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