3. Efectuar las operaciones de suma y resta de polinomios utilizando el método horizontal o vertical. a. (-3x 2 + 2xy + 10) + (9x 2 -10xy +5y-7) b. (10x 2 y + 7x 2 – 9y + 14) + (7x 2 y + 3x 2 – 8y + 10) c. (3x 2 + 2xy – 7y-12) - (7x 2 – 4xy + 8y+3) d. (15m 2 + 12mn + 20) – (9m 2 + 10mn + 5)
Respuestas a la pregunta
Respuesta:
a. (-3x 2 + 2xy + 10) + (9x 2 -10xy +5y-7)
Vamos a simplificar paso a paso.
(−3x)(2)+2xy+10+9x(2)−10xy+5y−7
=−6x+2xy+10+18x+−10xy+5y+−7
Combinar términos comunes:
=−6x+2xy+10+18x+−10xy+5y+−7
=(2xy+−10xy)+(−6x+18x)+(5y)+(10+−7)
=−8xy+12x+5y+3
solución:
=−8xy+12x+5y+3
b. (10x 2 y + 7x 2 – 9y + 14) + (7x 2 y + 3x 2 – 8y + 10)
Vamos a simplificar paso a paso.
10x(2)y+7x(2)−9y+14+7x(2)y+3x(2)−8y+10
=20xy+14x+−9y+14+14xy+6x+−8y+10
Combinar términos comunes:
=20xy+14x+−9y+14+14xy+6x+−8y+10
=(20xy+14xy)+(14x+6x)+(−9y+−8y)+(14+10)
=34xy+20x+−17y+24
solución:
=34xy+20x−17y+24
c.(3x 2 + 2xy – 7y-12) - (7x 2 – 4xy + 8y+3)
Vamos a simplificar paso a paso.
3x(2)+2xy−7y−12−(7x(2)−4xy+8y+3)
Distribuir el signo negativo:
=3x(2)+2xy−7y−12+−1(7x(2)−4xy+8y+3)
=3x(2)+2xy+−7y+−12+−1(7x(2))+−1(−4xy)+−1(8y)+(−1)(3)
=3x(2)+2xy+−7y+−12+−14x+4xy+−8y+−3
=6x+2xy+−7y+−12+−14x+4xy+−8y+−3
Combinar términos comunes:
=6x+2xy+−7y+−12+−14x+4xy+−8y+−3
=(2xy+4xy)+(6x+−14x)+(−7y+−8y)+(−12+−3)
=6xy+−8x+−15y+−15
solución:
=6xy−8x−15y−15
d. (15m 2 + 12mn + 20) – (9m 2 + 10mn + 5)
Vamos a simplificar paso a paso.
15m(2)+12mn+20−(9m(2)+10mn+5)
Distribuir el signo negativo:
=15m(2)+12mn+20+−1(9m(2)+10mn+5)
=15m(2)+12mn+20+−1(9m(2))+−1(10mn)+(−1)(5)
=15m(2)+12mn+20+−18m+−10mn+−5
=30m+12mn+20+−18m+−10mn+−5
Combinar términos comunes:
=30m+12mn+20+−18m+−10mn+−5
=(12mn+−10mn)+(30m+−18m)+(20+−5)
=2mn+12m+15
solución:
=2mn+12m+15