Schofield Hampton
11/20/2023 · High School
TALLER 1: EALIZAR LOS SIGUIENTES EJERCICIOS SEGUN EL CASO, USAR OS PROCEDIMIENTOS -ENTREGAR EN HOJAS DE BLOCK \( (6 x+y)^{2}= \) \( (9+4 x)^{2}= \) \( (7 x+11)^{2}= \) \( (a+b)^{2}= \) \( \left(1+3 x^{2}\right)^{2}= \) \( (2 x+3 y)^{2}= \) \( \left(a x^{2} x+b y^{2}\right)^{2}= \) \( \left(3 a^{3}+8 b^{4}\right)^{2}= \)
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Tutor-Verified Answer
Step-by-step Solution
Para resolver los ejercicios que has proporcionado, utilizaremos la fórmula del cuadrado de un binomio, que es:
\[
(a + b)^2 = a^2 + 2ab + b^2
\]
Ahora, aplicaremos esta fórmula a cada uno de los casos:
1. **Ejercicio:** \( (6x + y)^{2} \)
\[
= (6x)^{2} + 2(6x)(y) + (y)^{2}
\]
\[
= 36x^{2} + 12xy + y^{2}
\]
2. **Ejercicio:** \( (9 + 4x)^{2} \)
\[
= (9)^{2} + 2(9)(4x) + (4x)^{2}
\]
\[
= 81 + 72x + 16x^{2}
\]
3. **Ejercicio:** \( (7x + 11)^{2} \)
\[
= (7x)^{2} + 2(7x)(11) + (11)^{2}
\]
\[
= 49x^{2} + 154x + 121
\]
4. **Ejercicio:** \( (a + b)^{2} \)
\[
= a^{2} + 2ab + b^{2}
\]
5. **Ejercicio:** \( (1 + 3x^{2})^{2} \)
\[
= (1)^{2} + 2(1)(3x^{2}) + (3x^{2})^{2}
\]
\[
= 1 + 6x^{2} + 9x^{4}
\]
6. **Ejercicio:** \( (2x + 3y)^{2} \)
\[
= (2x)^{2} + 2(2x)(3y) + (3y)^{2}
\]
\[
= 4x^{2} + 12xy + 9y^{2}
\]
7. **Ejercicio:** \( (ax^{2} + by^{2})^{2} \)
\[
= (ax^{2})^{2} + 2(ax^{2})(by^{2}) + (by^{2})^{2}
\]
\[
= a^{2}x^{4} + 2abx^{2}y^{2} + b^{2}y^{4}
\]
8. **Ejercicio:** \( (3a^{3} + 8b^{4})^{2} \)
\[
= (3a^{3})^{2} + 2(3a^{3})(8b^{4}) + (8b^{4})^{2}
\]
\[
= 9a^{6} + 48a^{3}b^{4} + 64b^{8}
\]
Ahora tienes las soluciones a todos los ejercicios. Puedes escribirlas en hojas de block como se solicitó.
Quick Answer
1. \( (6x + y)^{2} = 36x^{2} + 12xy + y^{2} \)
2. \( (9 + 4x)^{2} = 81 + 72x + 16x^{2} \)
3. \( (7x + 11)^{2} = 49x^{2} + 154x + 121 \)
4. \( (a + b)^{2} = a^{2} + 2ab + b^{2} \)
5. \( (1 + 3x^{2})^{2} = 1 + 6x^{2} + 9x^{4} \)
6. \( (2x + 3y)^{2} = 4x^{2} + 12xy + 9y^{2} \)
7. \( (ax^{2} + by^{2})^{2} = a^{2}x^{4} + 2abx^{2}y^{2} + b^{2}y^{4} \)
8. \( (3a^{3} + 8b^{4})^{2} = 9a^{6} + 48a^{3}b^{4} + 64b^{8} \)
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