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

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

Evaluate

$$4$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\log_{10}\left(4\right)+2\right)^{2}.

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

Use the distributive property to multiply \log_{10}\left(4\right)+4 by \log_{10}\left(4\right).

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

To find the opposite of \left(\log_{10}\left(4\right)\right)^{2}+4\log_{10}\left(4\right), find the opposite of each term.

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

Combine \left(\log_{10}\left(4\right)\right)^{2} and -\left(\log_{10}\left(4\right)\right)^{2} to get 0.

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

Combine 4\log_{10}\left(4\right) and -4\log_{10}\left(4\right) to get 0.

$$4$$

Factor

$$2^{2}$$