Final answer:
The expression 64x12 + 27y3 factors into (4x4 + 3y)(16x8 - 12x4y + 9y2), using the sum of cubes formula a3 + b3 = (a + b)(a2 - ab + b2).
Step-by-step explanation:
To factor the algebraic expression 64x12 + 27y3, we recognize that it is a sum of cubes, since 64 is 43 and 27 is 33. Thus, the expression can be rewritten as (4x4)3 + (3y)3. The sum of cubes can be factored using the formula a3 + b3 = (a + b)(a2 - ab + b2). Applying this formula here gives us the factorization:
(4x4 + 3y)((4x4)2 - (4x4)(3y) + (3y)2)
Which simplifies to:
(4x4 + 3y)(16x8 - 12x4y + 9y2)
This result is the factored form of the original expression.