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.

$-19$

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