Question

alguém me ajuda por favor? eu preciso efetuar as multiplicações (os resultados estão na frente)​

Answer 1

Resposta:

Explicação passo-a-passo:

a)

$(\sqrt{2}-\sqrt{6})(\sqrt{2}+2\sqrt{6})=\sqrt{2}.\sqrt{2}+\sqrt{2}.2\sqrt{6}-\sqrt{6}.\sqrt{2}-\sqrt{6}.2\sqrt{6}\\\\\\(\sqrt{2}-\sqrt{6})(\sqrt{2}+2\sqrt{6})=2+2\sqrt{12}-\sqrt{12}-2.6\\\\(\sqrt{2}-\sqrt{6})(\sqrt{2}+2\sqrt{6})=2+\sqrt{12}-12\\\\(\sqrt{2}-\sqrt{6})(\sqrt{2}+2\sqrt{6})=-10+\sqrt{4.3}\\\\(\sqrt{2}-\sqrt{6})(\sqrt{2}+2\sqrt{6})=-10+\sqrt{4}.\sqrt{3}\\\\(\sqrt{2}-\sqrt{6})(\sqrt{2}+2\sqrt{6})=-10+2.\sqrt{3}$

b)

$(5-\sqrt{7})(5+\sqrt{7})=5^{2}-(\sqrt{7})^{2}=25-7=18$

c)

$(3\sqrt{5}-2)(\sqrt{5}+3)=3\sqrt{5}.\sqrt{5}+3\sqrt{5}.3-2\sqrt{5}-2.3\\\\(3\sqrt{5}-2)(\sqrt{5}+3)=3.5+9\sqrt{5}-2\sqrt{5}-6\\\\(3\sqrt{5}-2)(\sqrt{5}+3)=15+7\sqrt{5}-6\\\\(3\sqrt{5}-2)(\sqrt{5}+3)=9+7\sqrt{5}$

d)

$(4+\sqrt{13})(4-\sqrt{13})=4^{2}-(\sqrt{13})^{2}=16-13=3$