Final answer:
To simplify the expression 4a⁴+4a²-1, use the distributive property and recognize a perfect square trinomial.
Step-by-step explanation:
To simplify the expression 4a⁴+4a²-1, we can't combine any like terms because each term has a different exponent for a. However, we can rewrite the expression using the distributive property.
4a⁴+4a²-1 = 4a⁴ + (2a)² - 1
Now, we can see that the second term, (2a)², represents a perfect square trinomial. By factoring it, we get:
4a⁴ + (2a)² - 1 = 4a⁴ + 4a² - 1 = (2a² + 1)² - 1
So, the simplified form of 4a⁴+4a²-1 is (2a² + 1)² - 1.