How do you simplify $(\sqrt{5} - 2) (\sqrt{5} + 2)$ $(sqrt5-2)(sqrt5+2)$ ?

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Answer 1 · 2018-03-17T17:17:11

See a solution process below:

Use this rule for quadratics for this special case:

$(x + y) (x - y) = x^{2} - y^{2}$ $(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2$

Let:

Substitute as:

$(\sqrt{5} + 2) (\sqrt{5} - 2) \Rightarrow$ $(color(red)(sqrt(5)) + color(blue)(2))(color(red)(sqrt(5)) - color(blue)(2)) =>$

${(\sqrt{5})}^{2} - 2^{2} \Rightarrow$ $(color(red)(sqrt(5)))^2 - color(blue)(2)^2 =>$

$5 - 4 \Rightarrow$ $5 - 4 =>$

$1$ $1$

How do you simplify (sqrt5-2)(sqrt5+2)(√5−2)(√5+2)(sqrt5-2)(sqrt5+2)?