Instrucción l- Realiza la siguiente suma y resta de polinomias. \( \left(3 x^{2}-5 x+4\right)+(2 x-6)= \) \( \left(4 a^{2}-3 b^{2}\right)+\left(2 a b+b^{2}\right)+\left(b^{2}-a b-2 a^{2}\right)= \) \( \left(3 x^{3}+3 x^{2}-4 x+5\right)+\left(x^{3}-2 x^{2}+x-4\right)= \) \( \left(7 x^{2}-x-4\right)+\left(x^{2}-2 x-3\right)+\left(-3 x^{2}+4 x+5\right)= \) \( (2) \)
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¡Claro! Vamos a hacer esas operaciones de polinomios. Para la primera suma: \( \left(3 x^{2}-5 x+4\right)+(2 x-6)= 3 x^{2}+ (-5 x + 2 x)+ (4 - 6) = 3 x^{2} - 3 x - 2 \) Para la segunda: \( \left(4 a^{2}-3 b^{2}\right)+\left(2 a b+b^{2}\right)+\left(b^{2}-a b-2 a^{2}\right) = (4 a^{2} - 2 a^{2}) + (-3 b^{2} + b^{2}) + (2 a b - a b) = 2 a^{2} - 2 b^{2} + a b \) Para la tercera: \( \left(3 x^{3}+3 x^{2}-4 x+5\right)+\left(x^{3}-2 x^{2}+x-4\right) = (3 x^{3} + x^{3}) + (3 x^{2} - 2 x^{2}) + (-4 x + x) + (5 - 4) = 4 x^{3} + x^{2} - 3 x + 1 \) Para la cuarta: \( \left(7 x^{2}-x-4\right)+\left(x^{2}-2 x-3\right)+\left(-3 x^{2}+4 x+5\right) = (7 x^{2} + x^{2} - 3 x^{2}) + (-x - 2 x + 4 x) + (-4 - 3 + 5) = 5 x^{2} + x - 2 \) ¡Listo! Aquí tienes los resultados de cada operación.