How do you multiply (√2x - √6)²?

1 Answer
George C.
Jul 11, 2015

Use FOIL to find #(sqrt(2)x-sqrt(6))^2 = 2x^2-4sqrt(3)x+6#

Explanation:

#(sqrt(2)x-sqrt(6))^2#

#= (sqrt(2)x-sqrt(6))(sqrt(2)x-sqrt(6))#

#=underbrace(sqrt(2)x*sqrt(2)x)_color(blue)("First") + underbrace(sqrt(2)x*-sqrt(6))_color(blue)("Outside") + underbrace(-sqrt(6)*sqrt(2)x)_color(blue)("Inside") + underbrace(-sqrt(6)*-sqrt(6))_color(blue)("Last")#

#=2x^2-2sqrt(2)sqrt(6)x+6#

#=2x^2-2sqrt(2*6)x + 6#

#=2x^2-2sqrt(2^2*3)x+6#

#=2x^2-4sqrt(3)x+6#

...using #sqrt(ab) = sqrt(a)sqrt(b)# for #a, b >= 0#

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