Solucionar (log4+2)^2-(log4+4)*log4=

$$( \log 4 + 2 ) ^ { 2 } - ( \log 4 + 4 ) \cdot \log 4 =$$

Calcular

$$4$$

Pasos de la solución

Utilice el teorema binomial \left(a+b\right)^{2}=a^{2}+2ab+b^{2} para expandir \left(\log_{10}\left(4\right)+2\right)^{2}.

$$\left(\log_{10}\left(4\right)\right)^{2}+4\log_{10}\left(4\right)+4-\left(\log_{10}\left(4\right)+4\right)\log_{10}\left(4\right)$$

Usa la propiedad distributiva para multiplicar \log_{10}\left(4\right)+4 por \log_{10}\left(4\right).

$$\left(\log_{10}\left(4\right)\right)^{2}+4\log_{10}\left(4\right)+4-\left(\left(\log_{10}\left(4\right)\right)^{2}+4\log_{10}\left(4\right)\right)$$

Para calcular el opuesto de \left(\log_{10}\left(4\right)\right)^{2}+4\log_{10}\left(4\right), calcule el opuesto de cada término.

$$\left(\log_{10}\left(4\right)\right)^{2}+4\log_{10}\left(4\right)+4-\left(\log_{10}\left(4\right)\right)^{2}-4\log_{10}\left(4\right)$$

Combina \left(\log_{10}\left(4\right)\right)^{2} y -\left(\log_{10}\left(4\right)\right)^{2} para obtener 0.

$$4\log_{10}\left(4\right)+4-4\log_{10}\left(4\right)$$

Combina 4\log_{10}\left(4\right) y -4\log_{10}\left(4\right) para obtener 0.

$$4$$

Factorizar

$$2^{2}$$