Question

Factorise -
$9 {(2a - b)}^{2} - 4(2a - b) - 13$
CLUE -
The Answer is -
$(18a - 9b - 13)(2a - b + 1)$
Please Give the Answer with Step-by-step Explanation...

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Answer 1

Let ,

       2a - b = x  $\blue{\bigstar}$

Then , equation becomes 9x² - 4x - 13

Lets factorize the equation ,

⇒ 9x² - 4x - 13

Apply middle term splitting method ,

⇒ 9x² + 9x - 13x - 13        

Since , - 4 will be written as 9 - 13

⇒ 9x ( x + 1 ) - 13 ( x + 1 )

⇒ ( 9x - 13 ) ( x + 1 )

Sub. x value here ,

⇒ ( 9 ( 2a - b ) - 13 ) ( ( 2a - b ) + 1 )

⇒ ( 18a - 9b - 13 ) ( 2a - b + 1 )  $\pink{\bigstar}$

Hence ,

→ 9 ( 2a - b )² - 4 ( 2a - b ) - 13

  = ( 18a - 9b - 13 ) ( 2a - b + 1 ) $\orange{\bigstar}\ \; \bigstar\ \; \green{\bigstar}$

Answer 2

$\sf{\pink{\underline{\underline{\blue{SOLUTION:-}}}}}$

FACTORIES :-

• $\bf\red{9 {(2a - b)}^{2} - 4(2a - b) - 13}$

Let,

• 2a - b = X

☃️ Hence, the above equation be,

=> 9X² - 4X - 13

=> 9X² - 13X + 9X - 13

=> X (9X - 13) + 1 (9X - 13)

=> (9X - 13) (X + 1)

Put the value of “ X = 2a - b ” in the above equation,

=> [9 (2a - b) - 13] [(2a - b) + 1]

=> (18a - 9b - 13) (2a - b + 1)

$\pink\therefore\:\bf{\gray{\underline{\red{\boxed{\green{Required\:Answer\:\longrightarrow\:\atop{(18a\:-\:9b\:-\:13)\:(2a\:-\:b\:+\:1)}\:}}}}}}$