Question

(3√3 + 2√2 – 1) (3√3 - 2√2 +1) help!

Answer 1

Respuesta:

➜  $\left(3\sqrt{3}\:+\:2\sqrt{2}\:-\:1\right)\:\left(3\sqrt{3}\:-\:2\sqrt{2}\:+1\right)$   $=18+4\sqrt{2}$

• $\left(3\sqrt{3}\:+\:2\sqrt{2}\:-\:1\right)\:\left(3\sqrt{3}\:-\:2\sqrt{2}\:+1\right)$

Tienes que aplicar productos notables :

$=3\sqrt{3}\cdot \:3\sqrt{3}+3\sqrt{3}\left(-2\sqrt{2}\right)+3\sqrt{3}\cdot \:1+2\sqrt{2}\cdot \:3\sqrt{3}+2\sqrt{2}\left(-2\sqrt{2}\right)+2\sqrt{2}\cdot \:1+\left(-1\right)\cdot \:3\sqrt{3}+\left(-1\right)\left(-2\sqrt{2}\right)+\left(-1\right)\cdot \:1$

Aplica ley de signos : $+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab$

$=3\cdot \:3\sqrt{3}\sqrt{3}-3\cdot \:2\sqrt{3}\sqrt{2}+3\cdot \:1\cdot \sqrt{3}+2\cdot \:3\sqrt{2}\sqrt{3}-2\cdot \:2\sqrt{2}\sqrt{2}+2\cdot \:1\cdot \sqrt{2}-1\cdot \:3\sqrt{3}+1\cdot \:2\sqrt{2}-1\cdot \:$

Simplifica : $=3\cdot \:3\sqrt{3}\sqrt{3}-3\cdot \:2\sqrt{3}\sqrt{2}+3\cdot \:1\cdot \sqrt{3}+2\cdot \:3\sqrt{2}\sqrt{3}-2\cdot \:2\sqrt{2}\sqrt{2}+2\cdot \:1\cdot \sqrt{2}-1\cdot \:3\sqrt{3}+1\cdot \:2\sqrt{2}-1\cdot \: =18+4\sqrt{2}$