Final answer:
The expression 16x^3 - 54y^3 is factored using the difference of cubes formula resulting in (2x - 3y)(4x^2 + 6xy + 9y^2).
Step-by-step explanation:
The student's question appears to involve factoring a cubic polynomial expression. The given expression is 16x^3 - 54y^3. This is a difference of cubes, which can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2). In this case, a is 2x and b is 3y. Applying the formula to factor the expression, we get:
The given expression is 16x³-54y³. To simplify this expression, we can factor out the common factor of 2.
So, the expression becomes 2(8x³-27y³).
We can further factor this expression using the difference of cubes formula, which states a³-b³ = (a-b)(a²+ab+b²).
Applying this formula, we get 2[(2x)³-(3y)³] = 2(2x-3y)(4x²+6xy+9y²).
Therefore, the factored form of 16x³-54y³ is 2(2x-3y)(4x²+6xy+9y²).