To factorize the expression 81x⁴ - 256y⁴, we can recognize it as a difference of squares.
We know that 81x⁴ can be written as (9x²)² and 256y⁴ can be written as (16y²)².
The expression
81x⁴ - 256y⁴ can be rewritten as (
9x²)² - (1
6y²)².
Now we can use the difference of squares formula, which states that a² - b² = (a + b)(a - b).
Applying this formula, we have: (
9x²)² - (1
6y²)² = (
9x² + 1
6y²)(
9x² - 1
6y²) =
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