how do you solve this?? (3 + √5)^3?
(3 + √5)^3 and (3 − √5)^3
I don't get if I should do this?:
(3 + √5) (3 + √5) (3 + √5)
and multiply two at a time by foiling?
I don't know how to approach this!
Please help I need to solve it as (3 + √5)^3 and (3 − √5)^3
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Answers & Comments
You are right; you basically FOIL twice.
(3+√5)³ = (3+√5)(3+√5)(3+√5) =
(9+3√5+3√5+√25)(3+√5) =
(9+6√5+√5²)(3+√5) =
(9+5+6√5)(3+√5) = (14+6√5)(3+√5) =
42+14√5+18√5+6√25 =
42 + 32√5 +6√5² = 42 + 32√5 +(6•5) =
72 + 32√5
----------------------------------
(3-√5)³ = (3-√5)(3-√5)(3-√5) =
(9-3√5-3√5+√25)(3-√5) =
(9-6√5+5)(3-√5) = (14-6√5)(3-√5) =
42-14√5-18√5+6√25 =
42 - 32√5 + 6√5² = 42-32√5+(6•5) =
42-32√5+30 =
72 - 32√5
use the formulas (a+b)^3 and (a-b)^3 where a is 3 and b is root 5. simplify it and then multiply the terms.