Question

factories
9x² - у²+4у- 4​

Answer 1

To factories :

9x² - y² + 4y - 4

Identity used :

• ( a-b )² = a² + b² - 2ab
• (a+b)(a-b) = a² - b²

Solution :

9x² - y² + 4y - 4

➝ 9x² - ( y² + 4 - 4y)

➝ 9x² - [ (y)² + (2)² - (2)(y)(2) ]

➝ 9x² - [ (y -2)² ]

Now this is in form of a²-b² , where

• a² = 9x²
• b² = (y-2)²

➝ (3x)² - (y-2)²

➝ [ 3x + (y-2) ] × [ 3x - (y-2) ]

➝ ( 3x + y - 2 )×( 3x - y + 2 )

Therefore factors are,

• (3x + y - 2)
• (3x - y + 2)

________________________________

ANSWER :

9x² - y² + 4y - 4 = (3x + y - 2)(3x - y + 2)

Answer 2

$\gray{ \huge{ \sf \: solution}}$

To factories :

9x² - y² + 4y - 4

Identity used :

( a-b )² = a² + b² - 2ab

(a+b)(a-b) = a² - b²

Solution :

9x² - y² + 4y - 4

➝ 9x² - ( y² + 4 - 4y)

➝ 9x² - [ (y)² + (2)² - (2)(y)(2) ]

➝ 9x² - [ (y -2)² ]

Now this is in form of a²-b² , where

a² = 9x²

b² = (y-2)²

➝ (3x)² - (y-2)²

➝ [ 3x + (y-2) ] × [ 3x - (y-2) ]

➝ ( 3x + y - 2 )×( 3x - y + 2 )

Therefore factors are,

(3x + y - 2)

(3x - y + 2)

________________________________

ANSWER :

9x² - y² + 4y - 4 = (3x + y - 2)(3x - y + 2)