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2. Desarrolla la potencia \( (z+7)^{2} \). \( \begin{array}{ll}\text { a) } z^{2}-30 z+49 & \text { c) } z^{2}-14 z+49 \\ \text { b) } z^{2}+30 z+49 & \text { d) } z^{2}+14 z+49 \\ \text { 3. Obtén el resultado del siguiente binomio elevado al cuadrado: }(x+5)^{2} \text {. } \\ \begin{array}{ll}\text { a) } x^{2}+24 x+25 & \text { c) } x^{2}+10 x+25 \\ \text { b) } x^{2}+14 x+25 & \text { d) } x^{2}+20 x+25\end{array} \\ \text { 4. ¿Cuál es el segundo término del trinomio que resulta al desarrollar } \\ \text { (3b-2)2? } \\ \begin{array}{ll}\text { a) }-39 b & \text { c) }-12 b\end{array} \\ \text { 5. Al desarrollar a }(2 y+9 z)^{2} \text { se obtiene: } & \text { c) } 4 y^{2}+36 y z+81 z^{2} \\ \text { a) } y^{2}+72 y z+81 z^{2} & \text { d) } 4 y^{2}+18 y z+81 z^{2} \\ \text { b) } 2 y^{2}+68 y z+81 z^{2} & \end{array} \)

Ask by Bob Huang. in Mexico
Mar 15,2025

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1. \( (z + 7)^2 = z^2 + 14z + 49 \) (c) 2. \( (x + 5)^2 = x^2 + 10x + 25 \) (c) 3. El segundo término de \( (3b - 2)^2 \) es \( -12b \) (c) 4. \( (2y + 9z)^2 = 4y^2 + 36yz + 81z^2 \) (c)

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Beyond the Answer

Primero, al desarrollar la potencia \( (z+7)^{2} \), aplicamos la fórmula del cuadrado de un binomio: \( (a+b)^{2} = a^{2} + 2ab + b^{2} \). Entonces, obtenemos \( z^{2} + 14z + 49 \), así que la opción correcta es la c). Para el binomio \( (x+5)^{2} \), usando la misma fórmula, tenemos \( x^{2} + 10x + 25 \). Por lo tanto, la respuesta correcta es la c) también. ¡Así que ya tienes un truco para los binomios elevados al cuadrado!

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