Final answer:
The binomial 81m⁴-16 can be factored as (9m² + 4)(3m + 2)(3m - 2), by applying the difference of squares formula.
Step-by-step explanation:
To factor the binomial 81m⁴-16, we first notice that this is a difference of squares, which can be factored using the formula: a² - b² = (a+b)(a-b).
Here, a = 9m² and b = 4. Applying the difference of squares formula, we get: (9m² + 4)(9m² - 4).
The term (9m² - 4) can still be factored further using the difference of squares formula with a = 3m and b = 2. After applying the formula, our final factored form would be: (9m² + 4)(3m + 2)(3m - 2).
Learn more about factoring binomials