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Sagot :
Para restar el polinomio [tex]\( B \)[/tex] del polinomio [tex]\( A \)[/tex], es necesario realizar la resta término a término para cada uno de los términos presentes en los polinomios.
Los polinomios dados son:
[tex]\[ A = 4x^2 - 5x + 7y - 6 \][/tex]
[tex]\[ B = x^2 + 2x + 9y - 15 \][/tex]
Vamos a restar cada término correspondiente de los polinomios [tex]\( A \)[/tex] y [tex]\( B \)[/tex].
1. Término de [tex]\( x^2 \)[/tex]:
[tex]\[ 4x^2 - x^2 = (4 - 1)x^2 = 3x^2 \][/tex]
2. Término de [tex]\( x \)[/tex]:
[tex]\[ -5x - 2x = (-5 - 2)x = -7x \][/tex]
3. Término de [tex]\( y \)[/tex]:
[tex]\[ 7y - 9y = (7 - 9)y = -2y \][/tex]
4. Término constante:
[tex]\[ -6 - (-15) = -6 + 15 = 9 \][/tex]
Así, el polinomio resultante de restar [tex]\( B \)[/tex] de [tex]\( A \)[/tex] es:
[tex]\[ 3x^2 - 7x - 2y + 9 \][/tex]
Por lo tanto, la opción correcta es:
[tex]\[ \text{B) } 3x^2 - 7x - 2y + 9 \][/tex]
Los polinomios dados son:
[tex]\[ A = 4x^2 - 5x + 7y - 6 \][/tex]
[tex]\[ B = x^2 + 2x + 9y - 15 \][/tex]
Vamos a restar cada término correspondiente de los polinomios [tex]\( A \)[/tex] y [tex]\( B \)[/tex].
1. Término de [tex]\( x^2 \)[/tex]:
[tex]\[ 4x^2 - x^2 = (4 - 1)x^2 = 3x^2 \][/tex]
2. Término de [tex]\( x \)[/tex]:
[tex]\[ -5x - 2x = (-5 - 2)x = -7x \][/tex]
3. Término de [tex]\( y \)[/tex]:
[tex]\[ 7y - 9y = (7 - 9)y = -2y \][/tex]
4. Término constante:
[tex]\[ -6 - (-15) = -6 + 15 = 9 \][/tex]
Así, el polinomio resultante de restar [tex]\( B \)[/tex] de [tex]\( A \)[/tex] es:
[tex]\[ 3x^2 - 7x - 2y + 9 \][/tex]
Por lo tanto, la opción correcta es:
[tex]\[ \text{B) } 3x^2 - 7x - 2y + 9 \][/tex]
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