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What are the factors of $27 y 3 − 125 z 3$ ?

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(3 y − 5 z) 9 y 2 − 25 z 2 + 15 y z

(3 y + 5 z) 9 y 2 − 25 z 2 − 15 y z

(3 y + 5 z) 9 y 2 + 25 z 2 + 15 y z

(3 y − 5 z) 9 y 2 + 25 z 2 + 15 y z

answer is A.

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Detailed Solution

The given polynomial is,

27 y 3 − 125 z 3

We use the concept of algebraic identities to solve the given polynomial.

x 3 − y 3 = x − y x 2 + x y + y 2

So,
We can simplify it by expanding the bracket as,

⇒ 27 y 3 − 125 z 3 ⇒ 3 y 3 − 5 z 3

⇒ 3 y − 5 z 9 y 2 + 25 z 2 + 15 y z

Thus, the factors of

27 y 3 − 125 z 3

are

(3 y − 5 z) 9 y 2 + 25 z 2 + 15 y z .

Hence, option 1 is the correct option.

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