Question

Aplicando a propriedade distribuitiva, calcule:
a) (√3 + √2)^2
b) (1 - √7)^2
c) (4√2 + 5) (4√2 - 5)
d) (2 + √10)^2
e) (√11 + √7) ( √11 - √7)
f) (3√3 + √2)^2

Answer 1

$( \sqrt{3} + \sqrt{2} )( \sqrt{3} + \sqrt{2} ) = \\ \\ { \sqrt{3} }^{2} + 2 \sqrt{6} + { \sqrt{2} }^{2} = \\ \\ 3 + 2 \sqrt{6} + 2 = \\ \\ 5 + 2 \sqrt{6}$

$(1 - \sqrt{7} )(1 - \sqrt{7} ) = \\ \\ {1}^{2} - 2 \sqrt{7} - { \sqrt{7} }^{2} = \\ \\ 1 - 2\sqrt{7} - 7 = \\ \\ - 6 - 2 \sqrt{7}$

$(4 \sqrt{2} + 5)(4 \sqrt{2} - 5) = \\ \\ {(4 \sqrt{2} )}^{2} - 20 \sqrt{2} + 20 \sqrt{2} - 25 =\\ \\ 32 - 25 = 7$

$(2 + \sqrt{10})(2 + \sqrt{10}) = \\ \\ {2}^{2} + 4 \sqrt{10} + { \sqrt{10} }^{2} = \\ \\ 4 + 4 \sqrt{10} + 10 = \\ \\ 14 + 4\sqrt{10}$

$( \sqrt{11} + \sqrt{7} )( \sqrt{11} - \sqrt{7} ) = \\ \\ { \sqrt{11} }^{2} - \sqrt{77} + \sqrt{77} + { \sqrt{7} }^{2} = \\ \\ 11 + 7 = \\ \\ 18$

$(3 \sqrt{3} + \sqrt{2} )(3 \sqrt{3} + \sqrt{2} ) = \\ \\ {(3 \sqrt{3}) }^{2} + 6 \sqrt{6} + { \sqrt{2} }^{2} = \\ \\ 27 + 6 \sqrt{6} + 2 = \\ \\ 29 + 6 \sqrt{6}$