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What are the factors of $8 a b 2 − 18 a 3$ ?

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2 a 2 b − 3 a 2 b + 3 a

2 a 2 b − 3 a 2 b − 3 a

2 a 2 b + 3 a 2 b + 3 a

a 2 b − 3 a 2 b + 3 a

answer is A.

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Detailed Solution

The given expression is

8 a b 2 − 18 a 3

.
Rewrite the expression as,

8 a b 2 − 18 a 3 = 2 a (4 b 2 − 9 a 2) ⇒ 2 a ((2 b) 2 − (3 a) 2)

Use the identity,

a 2 − b 2 = (a + b) (a − b)

.
Here a=2b and b=3a.
Therefore,

2 a 2 b − 3 a 2 b + 3 a

Therefore, the expression

8 a b 2 − 18 a 3

can be factored as

2 a 2 b − 3 a 2 b + 3 a

.
Hence, option 1 is correct.

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