Question

(i square root of 10 - 4) (i square root of 10 + 4)
i as in imaginary i not variable

Answer 1

\[\left( i \sqrt{10}-4 \right)\left( i \sqrt{10} +4\right)\]

Answer 2

I would use
(a+b)(a-b)= a^2 - b^2

Answer 3

would you mind explaining a bit more?

Answer 4

do you know how to multiply two binomials (some people use FOIL) ?

Answer 5

oh yes sorry I was confused for a second

Answer 6

using just (a+b)(a-b) we get a^2 -ab +ab-b^2 which simplifies to a^2 - b^2
(we usually remember this as how to factor a *difference of squares* )

you can use FOIL, or you can use the "short-cut"
\[ \left( i \sqrt{10}-4 \right)\left( i \sqrt{10} +4\right) = ( i \sqrt{10})^2 - 4^2 \]

Answer 7

now you need to know what i*i is
and what \( \sqrt{10} \cdot \sqrt{10} \) is

Answer 8

i*i is -1
\[\sqrt{10} * \sqrt{10} is 10\]

Answer 9

ok, now simplify
\[ ( i \sqrt{10})^2 - 4^2 \]

Answer 10

-26

Answer 11

yes

Answer 12

thank you