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Factorise the expression $15 x 2 − 16 x y z − 15 y 2 z 2$ .

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3 x − 5 y z 5 x + 3 y z

3 x − 5 y z 5 x − 3 y z

3 x + 5 y z 5 x + 3 y z

3 x + 5 y z 5 x − 3 y z

answer is A.

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Detailed Solution

Given expression is

15 x 2 − 16 x y z − 15 y 2 z 2

.
To factorise the given expression, taking the product of the coefficient of

x 2

with the constant term,

15 × (− 15 y 2 z 2) = − 225 y 2 z 2

Now, finding the factors of

225 y 2 z 2

and treat them as the coefficient of x.

225 y 2 z 2 = 25 × 9 × y 2 × z 2 ⇒ 225 y 2 z 2 = 25 y z × 9 y z

Now, subtracting the factors,

25 y z − 9 y z = 16 y z

So, the quadratic trinomial is:
Question Image

Therefore, the factors of the given expression are

3 x − 5 y z 5 x + 3 y z

.
Hence, option 1 is correct.

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