How do you simplify this equation (8+√5)(8-√5)?

Question

jim_thompson5910 · Answer

Use the idea that

$$\Large (x+y)(x-y) = x^2 - y^2$$

anonymous · Answer

I don't get that..

jim_thompson5910 · Answer

Compare 

$$\Large (x+y)(x-y)$$

with 

$$\Large (8+\sqrt{5})(8-\sqrt{5})$$

jim_thompson5910 · Answer

Can you see how x  = 8 and $y = \sqrt{5}$ ???

anonymous · Answer

Right.

jim_thompson5910 · Answer

So 

$$\Large (x+y)(x-y) = x^2 - y^2$$ 

becomes

$$\Large (8+\sqrt{5})(8-\sqrt{5}) = (8)^2 - (\sqrt{5})^2$$

richyw · Answer

just expand it!$$(8+\sqrt{5})(8-\sqrt{5})$$
$$=64-8\sqrt{5}+8\sqrt{5}-5$$
$$=64-5=59$$

hero · Answer

Difference of Squares Formula:
$a^2 - b^2 = (a+b)(a-b)$

hero · Answer

In this case, $a = 8, b = \sqrt{5}$

hero · Answer

So by definition of difference of squares:
$a^2 - b^2     = (a+b)(a-b)$
$8^2 - \sqrt{5}^2 = (8 + \sqrt{5})(8-\sqrt{5})$
$64 - 5 = (8 + \sqrt{5})(8-\sqrt{5})$
$59 = (8 + \sqrt{5})(8-\sqrt{5})$

hero · Answer

Proof of squares: 

$a^2 - b^2 = (a+b)(a-b)$
             $=a(a-b)+b(a-b))$
             $=a^2 - ab + ab - b^2$
             $=a^2 - b^2$

hero · Answer

Further proof:

|dw:1341895795113:dw|