Question

factorise 9x^2+18x+8

Answer 1

$<b > Ello!¡$

Here's your answer

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To factorise of : 9x² + 18x + 8

Now ,

9x² + 18x + 8

= 9x² + 18x + 9 - 1 [ • ( 9 - 1 ) = 8 ]

= { ( 3x )² + 2 . 3x . 3 + ( 3 )² } - 1

[ • ( a + b )² = a² + 2ab + b² → Using this identity
Here , a = 3x , b = 3 ]

= ( 3x + 3 )² - ( 1 )² [ • ( 1 )² = 1 ]

= ( 3x + 3 + 1 ) ( 3x + 3 - 1 )

[ • a² - b² = ( a + b ) ( a - b ) → Using this identity
Here , a = ( 3x + 3 ) , b = 1 ]

= ( 3x + 4 ) ( 3x + 2 ) [ ★ Required answer ]

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Hope it helps!!

Answer 2

$9 {x}^{2} + 18x + 8 \\ = 9 {x}^{2} + 12x + 6x + 8 \\ = 3x(3x + 4) + 2(3x + 4) \\ = (3x + 4)(3x + 2)$