Macdonald Romero
11/12/2023 · High School
16. Desarrolla el siguiente binomio \( (x-7)^{2} \) Aplique la formula para resolver el binonio A) \( x^{2}-14 x+49 \) B) \( x^{2}+14 x+49 \) C) \( x^{2}-14 x-49 \) D) \( x^{2}+14 x-49 \)
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Tutor-Verified Answer
Step-by-step Solution
Para desarrollar el binomio \( (x-7)^{2} \), podemos aplicar la fórmula del cuadrado de un binomio, que es:
\[
(a - b)^{2} = a^{2} - 2ab + b^{2}
\]
En este caso, \( a = x \) y \( b = 7 \). Sustituyendo en la fórmula:
\[
(x - 7)^{2} = x^{2} - 2 \cdot x \cdot 7 + 7^{2}
\]
Calculamos cada término:
1. \( x^{2} \) se queda como está.
2. \( -2 \cdot x \cdot 7 = -14x \).
3. \( 7^{2} = 49 \).
Por lo tanto, el desarrollo del binomio es:
\[
(x - 7)^{2} = x^{2} - 14x + 49
\]
La respuesta correcta es:
A) \( x^{2} - 14x + 49 \)
Quick Answer
A) \( x^{2} - 14x + 49 \)
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