Question

Factorise the given expression completely : 4x^2 - 9y^2 + 12y - 4.​

Answer 1

The factor is $[tex]\Rightarrow (2x+3y-2)(2x-3y+2)$

Step-by-step explanation:

Given: $4x^2-9y^2+12y-4$

$\Rightarrow 4x^2-(9y^2-12y+4)$

$\Rightarrow 4x^2-[(3y)^2-2\cdot 3y\cdot 2+2^2]$    

• $\because a^2-2ab+b^2=(a-b)^2$

$\Rightarrow (2x)^2-(3y-2)^2$

• $\because a^2-b^2=(a+b)(a-b)$

$[tex]\Rightarrow (2x+3y-2)(2x-3y+2)$

#BAL

#ANSWERWITHQUALITY

Answer 2

Given :

4x² - 9y² + 12y - 4

To find :

Factorize 4x² - 9y² + 12y - 4

Solution :

4x² - 9y² + 12y - 4

4x² - (9y² - 12y + 4)

4x² - (9y² - 6y - 6y + 4)

4x² - [3y(3y - 2) - 2(3y - 2)]

4x² - (3y - 2)(3y - 2)

(2x)² - (3y - 2)²

Using formula : a² - b² = (a - b)(a + b)

(2x + 3y - 2)(2x - 3y + 2)