Final answer:
The sum of two cubes q³+216r³ is factored as (q+6r)(q²-6qr+36r²), using the sum of cubes formula a³+b³ = (a+b)(a²-ab+b²).
Step-by-step explanation:
The sum of two cubes, q³+216r³, can be factored using the formula for the sum of cubes, which is a³+b³ = (a+b)(a²-ab+b²). In our case, we can equivalently write 216r³ as (6r)³, recognizing that 216 is 6³. Now we apply the sum of cubes formula with a=q and b=6r.
The factored form is: (q+6r)(q²-6qr+36r²).
Remember the process of cubing of exponentials means we cube the digit term and multiply the exponent by three.