a^4−81 factor completely

Question

anonymous · Answer

use the following formula
$$\Large a^2-b^2=(a+b)(a-b)$$

lgbasallote · Answer

use difference of two squares
$$(a^4 - 81) \implies (a^2)^2 - (9)^2 \implies (a^2 + 9)(a^2 - 9)$$
notice how a^2 - 9 is another difference of two squares
$$(a^2 + 9)(a^2 - 9) \implies (a^2 + 9)(a^2 - (3^2)^2) \implies (a^2 + 9)(a+3)(a-3)$$
does that help?

lgbasallote · Answer

uhh that's supposed to be $(a^2 - 3^2)$not (3^2)^2

lgbasallote · Answer

$$(a^2 + 9)(a^2 - 9) \implies (a^2 + 9)(a^2 + 3^2) \implies (a^2 + 9)(a+3)(a-3)$$

anonymous · Answer

(a^2+9)(a+3)(a−3) is not correct when i type it in @lgbasallote

lgbasallote · Answer

that's because there's one more step

lgbasallote · Answer

$$a^2 + 9 \implies (a+3i)(a-3i)$$

lgbasallote · Answer

so what do you think will be the final answer?

anonymous · Answer

(a+3)(a−3)?

lgbasallote · Answer

no

lgbasallote · Answer

i told you the answer is $$(a^2 + 9)(a+3)(a-3)$$
then i told you $$(a^2 + 9) = (a+3i)(a-3i)$$
now try to think what you should do to get the final answer

anonymous · Answer

(a+3i)(a−3i)(a+3)(a−3)? but where do the "i" come into play

lgbasallote · Answer

what do you mean?

lgbasallote · Answer

why there's an i?

lgbasallote · Answer

and yes that answer is right

anonymous · Answer

no when i type in (a+3i)(a−3i)(a+3)(a−3) thats not correct

lgbasallote · Answer

how about (a^2 + 9)(a^2 -9)

anonymous · Answer

nope

anonymous · Answer

try doing this one i cant do, 27a^3−8b^3

anonymous · Answer

@lgbasallote

lgbasallote · Answer

if you just want some answers then go here it's much faster than me http://www.wolframalpha.com/input/?i=27a%5E3%E2%88%928b%5E3