How do you simplify #(5 + 2sqrt7)^2#?

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Answer 1 · 2017-08-08T01:50:00

See a solution process below:

We can use this rule to simplify the expression:

#(color(red)(x) + color(blue)(y))^2 = color(red)(x)^2 + 2color(red)(x)color(blue)(y) + color(blue)(y)^2#

Substituting #color(red)(5)# for #color(red)(x)# and substituting #color(red)(2sqrt(7))# for #color(blue)(y)# gives:

#(color(red)(5) + color(blue)(y))^2 => color(red)(5)^2 + (2 * color(red)(5) * color(blue)(2sqrt(7))) + color(blue)((2sqrt(7)))^2 =>#

#25 + 20sqrt(7) + (4 * 7) =>#

#25 + 20sqrt(7) + 28 =>#

#25 + 28 + 20sqrt(7) =>#

#53 + 20sqrt(7)#