\( \begin{array}{ll}\text { 12. } & x^{4}+9 x y^{3}-11 y^{4} \text { restar }-8 x^{3} y-6 x^{2} y^{2}+20 y^{4} \text {. } \\ \text { 13. } & a+b+c-d \text { restar }-a-b+c-d . \\ \text { 14. } & a b+2 a c-3 c d-5 d e \text { restar }-4 a c+8 a b-5 c d+5 d e . \\ \text { 15. } & x^{3}-9 x+6 x^{2}-19 \text { restar }-11 x^{2}+21 x-43+6 x^{3} . \\ \text { 16. } & y^{5}-9 y^{3}+6 y^{2}-31 \text { restar }-11 y^{4}+31 y^{3}-8 y^{2}-19 y .\end{array} \)
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Beyond the Answer
To make polynomial subtraction easier, remember that you can think of it as adding the opposite. This means you can change the signs of all terms of the second polynomial and then combine like terms. Keep an eye out for those pesky signs; they can easily turn a positive number into a negative one and vice versa—always double-check those calculations for accuracy! A fun way to enhance your polynomial skills is to try drawing a visual representation of polynomial expressions on graph paper. This can help you see the connections between different terms, especially if you categorize them by degree or type. Additionally, there are tons of resources online like educational videos and interactive polynomial solvers that can help solidify your understanding and keep you engaged!
