Question

Factories x² - y² - 9z² + 6yz
1. (x + y - 3z) (x + y + 3z)
2. (x - y - 3z) (x - y + 2z)
3. (x - y + 3z) (x + y - 3z) 
4. None of these

Answer 1

Correct Answer - Option 3 : (x - y + 3z) (x + y - 3z) 

Concept:

When we factorize an algebraic expression, we write it as a product of factors. These factors may be numbers, algebraic variables, or algebraic expressions.

Formula: 

(x - y)² = x² + y² - 2xy

x² - y² = (x + y) (x - y)

Calculation:

given equation is x2 - y2 - 9z2 + 6yz

⇒  x2 - (y2 + 9z2 - 6yz)

⇒ x2 - [(y)2 + (3z)2 - 2(y)(3z)] [∵ (x - y)2 = x2 + y2 - 2xy]

⇒ x2 - (y - 3z)² 

⇒  (x - (y - 3z)) (x + (y - 3z))  [∵ x2 - y2 = (x + y) (x - y)]

⇒  (x - y + 3z) (x + y - 3z)