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Which of the following is the factorized form of the polynomial ${(3 x + 5 y)}^{2} - 4 z^{2}$ ?

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(3 x - 5 y + 2 z) (3 x - 5 y - 2 z)

(3 x + 5 y + 2 z) (3 x - 5 y + 2 z)

(3 x + 5 y + 2 z) (3 x + 5 y - 2 z)

(3 x - 5 y + 2 z) (3 x + 5 y - 2 z)

answer is D.

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Detailed Solution

The given polynomial is

{(3 x + 5 y)}^{2} - 4 z^{2} .

The given polynomial can be written as

{(3 x + 5 y)}^{2} - {(2 z)}^{2} .

We know that

a^{2} - b^{2} = (a + b) (a - b) .

Consider here

a = 3 x + 5 y and b = 2 z .

Therefore,

{(3 x + 5 y)}^{2} - {(2 z)}^{2} = (3 x + 5 y + 2 z) (3 x + 5 y - 2 z)

Thus the polynomial

{(3 x + 5 y)}^{2} - 4 z^{2}

could be factorized as

(3 x + 5 y + 2 z) (3 x + 5 y - 2 z) .

Therefore, option (4) is the correct option.

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