Question

factorise 4x^2-y^2+6y-9

Answer 1

$4 {x}^{2} - {y}^{2} + 6y - 9$

$4 {x}^{2} - ( {y}^{2} - 6y + 9)$

$4 {x}^{2} - {(y - 3)}^{2}$

$(2x - (y - 3)) \: (2x + (y - 3))$

$(2x - y + 3) \: (2x + y - 3)$

Answer 2

4x² - y² + 6y - 9 = (2x - y + 3) (2x + y - 3)

Given :

The expression 4x² - y² + 6y - 9

To find :

Factorise the expression

Formula :

a² - b² = ( a + b ) ( a - b )

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

4x² - y² + 6y - 9

Step 2 of 2 :

Factorise the expression

$\sf 4 {x}^{2} - {y}^{2} + 6y - 9$

$\sf = 4 {x}^{2} - ( {y}^{2} - 6y + 9)$

$\sf = {(2x)}^{2} - {(y - 3)}^{2}$

$\sf = (2x - y + 3) (2x + y - 3)$

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