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𝑥^6 − 729

Answer:

𝑥^6 − 729

According to the equation,

𝑎^3 − 𝑏^3 = (𝑎 − 𝑏)(𝑎^2 + 𝑎𝑏 + 𝑏^2)

So we get,

𝑥^6 − 729

= (𝑥^2)^3 − 9^3

Using the equation,

= (𝑥^2 − 9)((𝑥^2)^2 + (𝑥^2)(9) + 9^2)

= (𝑥^2 − 9)(𝑥^4 + 9𝑥^2 + 81)

Based on the equation,

= (𝑥 + 3)(𝑥 − 3)[(𝑥^2 + 9)^2 − (3𝑥)^2]

On further simplification

= (𝑥 + 3)(𝑥 − 3)(𝑥^2 + 9 + 3𝑥)(𝑥^2 + 9 − 3𝑥)

"hello guys welcome back to your homework
i'm revant kumar working as a tutor at
leader
so today we are going to solve and
explore one more very interesting
question
and it's really very easy to solve also
so let's see how we can do it here
so now we have given here it as x cube
minus 729
x power 6 x 6 minus 129
so x power 6 and 729 are also perfect
squares only
if you are writing them in another way
so x square
whole cube minus 9 whole cube
now they are perfect square only right
so now it is in the exact format of
a cube minus b cube again so a q minus b
q formula is equals to a minus b
of a squared plus a b
plus b square so just substitute these
values here a
and b in this then you will be getting
the answer as
x square minus 9 x square minus 9
of x square whole square plus
x square multiplied by 9 plus 9
whole square so that is equals to x
square minus 9
of x power 4 plus
9 x square plus 81
so that is our final answer here so i
hope you have everything clear like what
i've done here
if you have any doubts please comment
below don't forget to subscribe to this
channel
thank you so much for watching this stay
tuned thank you"

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