Final answer:
To simplify the expression 7a⁴ + 12a² - 27, separate each term and simplify them individually.
Step-by-step explanation:
The given expression is 7a⁴ + 12a² - 27. To simplify this expression, we can't combine the terms since the variables have different powers. So, we treat each term separately.
The first term, 7a⁴, cannot be simplified further.
The second term, 12a², is in the form of ka², where k = 12. It is a perfect square trinomial, and we can factor it as (a)² = a * a. So, the simplified form of this term is 2(a)² = 2a * 2a = 4a².
The last term, 27, doesn't have any variables, so it remains unchanged.
Putting it all together, the simplified expression is 7a⁴ + 4a² - 27.