12. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.5.058. 24 Use vertical form to subtract the polynomials. (Simplify your answer completely.) Subtract \( 6 y^{2}-9 y+9 \) from \( 9 y^{2}+9 y+19 \). SUBMIT ANSWER 13. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.5.066.

To subtract the polynomials \( 6y^2 - 9y + 9 \) from \( 9y^2 + 9y + 19 \), write them in vertical form, aligning like terms: ``` 9y^2 + 9y + 19 - (6y^2 - 9y + 9) ------------------- ``` Now, perform the subtraction: 1. For the \(y^2\) terms: \(9y^2 - 6y^2 = 3y^2\) 2. For the \(y\) terms: \(9y - (-9y) = 9y + 9y = 18y\) 3. For the constant terms: \(19 - 9 = 10\) So, the simplified answer is \(3y^2 + 18y + 10\). In the world of polynomials, subtraction isn’t just about numbers; it’s about managing the signs of your terms! Always remember to distribute the negative sign to all terms in the polynomial you are subtracting, as this can be a common pitfall. Mistakes can easily occur when it comes to flipping signs, so double-check your work! If you're keen to dive deeper into polynomial operations, grabbing a textbook like "Algebra and Trigonometry" by Michael Sullivan can provide a wealth of practice problems and explanations. There are also plenty of online resources such as Khan Academy that offer interactive exercises to master polynomial subtraction in a jiffy!