Question

(4-sqrt6)(sqrt6+4)

Answer 1

\[(4-\sqrt{6})(\sqrt{6}+4)\]You can rewrite this as\[(4-\sqrt{6})(4+\sqrt{6})\]Does that give you any ideas?

remember, \[(a+b)(a-b) = a^2-ab+ab-b^2 = a^2-b^2\]

Answer 2

im sorry, im still lost

Answer 3

or use the foil method to make it easier for you to understand :)

Answer 4

okay, if you have two numbers a, b and you multiply (a-b)(a+b), you can do it the long way, or you can remember that \[(a-b)(a+b) = a^2 +ab -ab -b^2 = a^2-b^2\]

You have the same setup, with \(a = 4, b = \sqrt{6}\)
So, you have a choice: you can multiply it out, like the other poster suggests, or you can just fill in the blanks in \[a^2-b^2\]

Answer 5

What is \((4)^2\)?

What is \((\sqrt{6})^2\)?

Answer 6

16,6?

Answer 7

right! so what is 16-6?

Answer 8

10 is your answer. Doesn't that beat doing this?

\[(4-\sqrt{6})(\sqrt{6} + 4) = 4\sqrt{6}+4*4 -\sqrt{6}\sqrt{6}-4\sqrt{6} = \]

Answer 9

definitely, thank you.

Answer 10

so that pattern is called a difference of squares. it is very important that you learn to recognize it, because it will come up over and over again in algebra, trig, calculus