Question

factorise the given one

Answer 1

Question :

Factorise (3x - 4)² - (3x - 4) - 42

Answer :

( 3x + 2 ) ( 3x - 11 )

Step-by-step explanation :

( 3x - 4 )² - ( 3x - 4 ) - 42

Let ( 3x - 4 ) be 'a', now

⇒ (  3x - 4 )² - ( 3x - 4 ) - 42

⇒ a² - a - 42

⇒ a² - 7a + 6a - 42

⇒ a ( a - 7 ) + 6 ( a - 7 )

⇒ ( a + 6 ) ( a - 7 )

Now, putting the value of a as ( 3x - 4 ),

⇒ ( a + 6 ) ( a - 7 )

⇒[ ( 3x - 4 ) + 6 ] [ ( 3x - 4 ) - 7 ]

⇒ ( 3x + 2 ) ( 3x - 11 )

Hence, the answer is ( 3x + 2 ) ( 3x - 11 ).

Answer 2

$\sf {Answer : (3x + 2)(3x - 11)}$

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Factorise :

$\sf{(3x - 4) {}^{2} - (3x - 4) - 42}$

Simplify it :

$\sf{(3x - 4) {}^{2} - 3x + 4 - 42}$

$\sf{Using ( a - b )^2 = a^2 - 2ab + b^2}$

$\sf{3x {}^{2} -( 2 \times 3x \times 4 )- 3x - 38}$

Simplify the sum further :

$\sf{ = 16 + (3) {}^{2}x {}^{2} - 24x - 3x - 38}$

$\sf{ = 16 + 9x {}^{2} - 27x - 38}$

Subtracting 16 and 38 :

$\sf{ = 9x {}^{2} - 27x - 22}$

Finally, Factorising it to get :


$\sf{ = (3x + 2)(3x - 11)}$



Hence, Factorised .

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