How do you simplify #(3 – 2sqrt7)(3 + 2sqrt7)#?

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Answer 1 · 2017-01-26T02:52:46

#(3-2sqrt7)(3+2sqrt7)=-19#

Simplify #(3-2sqrt7)(3+2sqrt7)#.

This is a difference of squares problem, #a^2-b^2#, where #a=3#, and #b=2sqrt7#.

#3^2-(2sqrt7)^2#

Simplify.

#9-(2sqrt7)^2#

Apply multiplication distributive property, #(xy)^m=x^my^m#.

#9-2^2sqrt7^2#

Simplify.

#9-4xx(sqrt7)^2#

Apply square root rule, #(sqrtx)^2=x#.

Simplify.

#9-4xx7#

Simplify. Apply order of operations and multiply #4xx7# first.

#9-28#

Simplify.

#-19#