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

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

Calcula

$$4$$

Passos de solució

Utilitzeu el teorema del binomi \left(a+b\right)^{2}=a^{2}+2ab+b^{2} per desenvolupar \left(\log_{10}\left(4\right)+2\right)^{2}.

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

Utilitzeu la propietat distributiva per multiplicar \log_{10}\left(4\right)+4 per \log_{10}\left(4\right).

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

Per trobar l'oposat de \left(\log_{10}\left(4\right)\right)^{2}+4\log_{10}\left(4\right), cerqueu l'oposat de cada terme.

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

Combineu \left(\log_{10}\left(4\right)\right)^{2} i -\left(\log_{10}\left(4\right)\right)^{2} per obtenir 0.

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

Combineu 4\log_{10}\left(4\right) i -4\log_{10}\left(4\right) per obtenir 0.

$$4$$

Factoritzar

$$2^{2}$$