Løs (log4+2)^2-(log4+4)*log4=

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

Evaluer

$$4$$

Løsningsvejledning

Brug binomialsætningen \left(a+b\right)^{2}=a^{2}+2ab+b^{2} til at udvide \left(\log_{10}\left(4\right)+2\right)^{2}.

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

Brug fordelingsegenskaben til at multiplicere \log_{10}\left(4\right)+4 med \log_{10}\left(4\right).

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

For at finde det modsatte af \left(\log_{10}\left(4\right)\right)^{2}+4\log_{10}\left(4\right) skal du finde det modsatte af hvert led.

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

Kombiner \left(\log_{10}\left(4\right)\right)^{2} og -\left(\log_{10}\left(4\right)\right)^{2} for at få 0.

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

Kombiner 4\log_{10}\left(4\right) og -4\log_{10}\left(4\right) for at få 0.

$$4$$

Faktoriser

$$2^{2}$$