Question

One of the factors of ( 36x^2 - 1 ) + ( 1 + 6x )^2 = ?

Answer 1

( 36x² - 1 ) + ( 1 + 6x² )

=> [ ( 6x )² - 1² ] + ( 1 + 6x )²



We know, ( a² - b² ) = ( a + b ) ( a - b )


Applying formula,



=> ( 6x + 1 ) ( 6x - 1 ) + ( 6x + 1 )²

=> ( 6x + 1 ) ( 6x - 1 + 6x + 1 )

=> ( 6x + 1 ) ( 12x )

=> 12x( 6x + 1 )




Factors : 12x and ( 6x + 1 )


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Answer 2

The factors of (36x² - 1) + (1 + 6x)² are (6x + 1) (12x)  

Given:

(36x² - 1) + (1 + 6x)²

To find:

Factors of given equation

Solution:

Given (36x² - 1) + (1 + 6x)²  

As we know

36 = 6² ⇒ 36x² = (6x)²  

Then the given equation can be written as given below

⇒ (6x)² - 1² + (1+6x)²  

From algebraic identity (a²-b²) = (a+b)(a-b)

⇒ (6x+1)(6x-1) + (1+6x)²  

Take (6x+1) common

⇒ (6x+1) [ 6x - 1 + 1 + 6x ]

⇒ (6x + 1) (12x)  

Therefore,

The factors of (36x² - 1) + (1 + 6x)² are (6x + 1) (12x)  

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