Final answer:
The quadratic trinomial 9y² - 121x⁴ factors completely into the product of two binomials, (3y - 11x²)(3y + 11x²). This is achieved by utilizing the difference of squares factoring formula: a² - b² = (a - b)(a + b).
Step-by-step explanation:
The equation given, 9y² - 121x⁴, is a difference of two squares. In mathematics, a difference of squares is a squared number subtracted from another squared number, and it can be factored into the product of two binomials. The structure of this formula is a² - b² = (a-b)(a+b).
In this case, 9y² = (3y)² and 121x⁴ = (11x²)². Plugging into the formula gives: (3y - 11x²)(3y + 11x²). So, when factoring the quadratic trinomial 9y² - 121x⁴ completely, your main answer is (3y - 11x²)(3y + 11x²).
To make sure this solution is correct, you can multiply the binomials back together to see if you obtain the original expression. If the original equation is regained, this confirms the accuracy of the solution.
In conclusion, always remember that the difference of squares is a useful formula for factoring certain types of expressions in algebra.
Learn more about Factoring Quadratic Trinomials