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The factored form of $4 − 36 x 2 =$ [[1]].

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answer is 4 ( 1 − 3 X ) ( 1 + 3 X ).

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Detailed Solution

The factored form of

4 − 36 x 2 =

4 (1 − 3 x) (1 + 3 x)

.
The given expression is as follows,

4 − 36 x 2

.
It can be observed that 4 is a term which divides both the terms in the equation.
So, it is the HCF, and hence, factoring it out, we get,

4 − 36 x 2 = 4 1 − 9 x 2 = 4 12 − 3 x 2

Now, it can be observed that the expression inside the parentheses is of the general form

(a 2 − b 2)

, where

a = 1

and

b = 3 x

.
So, using the identity

a 2 − b 2 = (a + b) (a − b)

, we get the factored form of the expression as follows,

4 − 36 x 2 = 4 1 − 9 x 2 = 4 12 − 3 x 2 = 4 1 − 3 x 1 + 3 x

Hence, the blank will be filled by the expression

4 (1 − 3 x) (1 + 3 x)

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