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How many algebraic identities are required to factorize the polynomial $25 x 2 − 64 y 2$ ?

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answer is B.

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Detailed Solution

The given polynomial is

25 x 2 − 64 y 2 .

The given polynomial can be written as,

25 x 2 − 64 y 2 = 5 x 2 − 8 y 2

We know that

a 2 − b 2 = a − b a + b .

Therefore, the given polynomial can be solved using this formula by taking

a = 5 x and b = 8 y .

Therefore, the factorized form of the polynomial

25 x 2 − 64 y 2

5 x − 8 y 5 x + 8 y .

Since we use only 1 algebraic identity to factorize this, therefore option (2) is correct.

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