Final answer:
To multiply ((4/9)y² - (1/4))² using the binomial squares pattern, you find A² as (16/81)y⁴, 2AB as (4/9)y², and B² as 1/16. Combine these to get the final result: (16/81)y⁴ - (4/9)y² + 1/16.
Step-by-step explanation:
To multiply ((4/9)y² - (1/4))² using the binomial squares pattern, we need to recognize that this expression is a perfect square binomial, which means it takes the form of (A - B)². The binomial squares pattern tells us that (A - B)² equals A² - 2AB + B². Applying this to our expression, let A = (4/9)y² and B = (1/4).
First, we square A to get A²: ((4/9)y²)² = (4/9)² * (y²)² = 16/81 * y⁴.
Next, we find 2AB: 2 * (4/9)y² * (1/4) = (8/36)y² = (2/9)y².
Finally, we square B to get B²: ((1/4))² = 1/16.
Now, we combine these three results to get the final expression: (16/81)y⁴ - 2*((2/9)y²) + 1/16. Simplifying the middle term 2*((2/9)y²) gives (4/9)y², and the entire expression simplifies to (16/81)y⁴ - (4/9)y² + 1/16.