Final answer:
To square the binomial (4xy² - 5z³)², we use the formula (a - b)² to get 16x² y⁴ - 40x¹y² z³ + 25z⁶.
Step-by-step explanation:
The question asks us to square the binomial (4xy² - 5z³)².
Squaring a binomial is a concept in algebra that means we need to multiply the binomial by itself. The formula for squaring a binomial (a - b)² is a² - 2ab + b².
Therefore, we can expand the binomial (4xy² - 5z³)² using this formula:
- First, we find the square of the first term: (4xy² )² = 16x² y⁴.
- Second, we find twice the product of the two terms: 2 × (4xy² ) × (-5z³) = -40x¹y² z³.
- Finally, we find the square of the second term: (-5z³)² = 25z⁶.
Putting it all together, we get the expanded form of the binomial: 16x² y⁴ - 40x¹y² z³ + 25z⁶