Final answer:
The polynomial 8x³ - 729y³ can be factored into two polynomials A and B, with A being (2x - 9y) and B being (4x² + 18xy + 81y²) using the difference of cubes formula.
Step-by-step explanation:
To factor the polynomial 8x³ - 729y³ into the product of two polynomials, A and B, where the degree of A is greater than the degree of B, we first observe that this expression is a difference of cubes. The difference of cubes can be factored using the formula a³ - b³ = (a - b)(a² + ab + b²). In our case, 8x³ is the cube of 2x and 729y³ is the cube of 9y.
The factored form of the given polynomial using the difference of cubes formula is:
A = (2x - 9y)
B = (4x² + 18xy + 81y²)
Polynomial A has the greater degree than polynomial B. Given that all terms are cubed correctly, and obeying the exponents multiplication rule, the expression for A and B are determined correctly.