How do you multiply $(2 \sqrt{7} + \sqrt{5}) (\sqrt{3} + \sqrt{2}) (2 \sqrt{7} - \sqrt{5})$ $(2sqrt7+sqrt5)(sqrt3+sqrt2)(2sqrt7-sqrt5)$ ?

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Answer 1 · 2015-06-05T23:19:31

It's easiest to multiply $(2 \sqrt{7} + \sqrt{5}) (2 \sqrt{7} - \sqrt{5})$ $(2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))$ first...

$(2 \sqrt{7} + \sqrt{5}) (2 \sqrt{7} - \sqrt{5})$ $(2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))$ is of the form

$(a + b) (a - b) = a^{2} - b^{2}$ $(a+b)(a-b) = a^2 - b^2$ with $a = 2 \sqrt{7}$ $a=2sqrt(7)$ and $b = \sqrt{5}$ $b=sqrt(5)$

So:

$(2 \sqrt{7} + \sqrt{5}) (2 \sqrt{7} - \sqrt{5})$ $(2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))$

$= {(2 \sqrt{7})}^{2} - {\sqrt{5}}^{2} = (4 \cdot 7) - 5 = 28 - 5 = 23$ $=(2sqrt(7))^2-sqrt(5)^2 = (4*7)-5 = 28 - 5 = 23$

Then

$(2 \sqrt{7} + \sqrt{5}) (\sqrt{3} + \sqrt{2}) (2 \sqrt{7} - \sqrt{5})$ $(2sqrt(7)+sqrt(5))(sqrt(3)+sqrt(2))(2sqrt(7)-sqrt(5))$

$= (2 \sqrt{7} + \sqrt{5}) (2 \sqrt{7} - \sqrt{5}) (\sqrt{3} + \sqrt{2})$ $= (2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))(sqrt(3)+sqrt(2))$

$= 23 (\sqrt{3} + \sqrt{2}) = 23 \sqrt{3} + 23 \sqrt{2}$ $=23(sqrt(3)+sqrt(2)) = 23sqrt(3)+23sqrt(2)$

How do you multiply (2√7+√5)(√3+√2)(2√7−√5)(2sqrt7+sqrt5)(sqrt3+sqrt2)(2sqrt7-sqrt5)?