A conference room is in the shape of a rectangle. Its floor has a length of (x − 4) meters and a width of (3x − 1) meters:(x − 4)(3x − 1)Which of the following simplified expressions represents the area of the floor of the conference room in square meters? x2 − 13x + 4 3x2 − 13x + 4 3x2 − 11x + 4 x2 − 12x + 4
Question
A conference room is in the shape of a rectangle. Its floor has a length of (x − 4) meters and a width of (3x − 1) meters:(x − 4)(3x − 1)Which of the following simplified expressions represents the area of the floor of the conference room in square meters? x2 − 13x + 4 3x2 − 13x + 4 3x2 − 11x + 4 x2 − 12x + 4
Solution
Para encontrar la expresión simplificada que representa el área del piso de la sala de conferencias, debemos multiplicar las dos dimensiones dadas: (x − 4) y (3x − 1).
Paso 1: Utilizamos la propiedad distributiva (también conocida como el método FOIL para binomios) para multiplicar las dos expresiones.
(x − 4)(3x − 1)
Paso 2: Multiplicamos cada término en el primer paréntesis por cada término en el segundo paréntesis.
x * 3x + x * (-1) + (-4) * 3x + (-4) * (-1)
Paso 3: Realizamos las multiplicaciones.
3x^2 - x - 12x + 4
Paso 4: Combinamos los términos semejantes.
3x^2 - 13x + 4
Por lo tanto, la expresión simplificada que representa el área del piso de la sala de conferencias en metros cuadrados es:
3x^2 - 13x + 4
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