Final answer:
The solutions to the equation 4y⁴ -16y² = 0 are y = 0 and y = ±2.
Step-by-step explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4, b = 0, and c = -16. In order to solve this equation, we can use factoring. First, let's factor out the common factor 4y²:
4y²( y² - 4) = 0
Now we can solve each factor separately:
1. 4y² = 0:
y = 0
2. y² - 4 = 0:
y² = 4
y = ±2
Therefore, the solutions to the equation 4y⁴ -16y² = 0 are y = 0 and y = ±2.