Which of the following is the correct factorization of the polynomial below?

C. (p - 6q)(p² + 6pq + 36q²)

Step-by-step explanation:

Equation at the end of step 1

Trying to factor as a Difference of Cubes:

Factoring:  p^3 - 216q^3

Theory: A difference of two perfect cubes, a^3 - b^3 can be factored into

(a-b) • (a^2 +ab +b^2)

Proof:

Check:  216 is the cube of 6

Check:  p^3 is the cube of p^1

Check:  q^3 is the cube of q^1

Factorization is:

Trying to factor a multi variable polynomial :

Factoring: p^2 + 6pq + 36q^2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final Result:

(p - 6q)(p² + 6pq + 36q²)

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step-by-step explanation:

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step-by-step explanation: