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What are the factors of $343 + 125 b 3$ ?

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7 + 5 b 49 + 35 b + 25 b 2

7 − 5 b 49 + 35 b + 25 b 2

7 + 5 b 49 − 35 b + 25 b 2

7 + 5 b 49 + 35 b − 25 b 2

answer is A.

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Detailed Solution

The given expression is

343 + 125 b 3

.
Use the formula

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

.
Rewrite the expression as,

343 + 125 b 3 = 73 + 5 b 3

.
Use the formula

, Here a=7 and b=5b.
Substitute the values in the formula.

73 + 5 b 3 = 7 + 5 b 72 + 7 5 b + 5 b 2 ⇒ 7 + 5 b 49 + 35 b + 25 b 2

Therefore, the factors of

343 + 125 b 3

are

7 + 5 b 49 + 35 b + 25 b 2

.
Hence, option 1 is correct.

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