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(𝑥 + 2)^3 + (𝑥 − 2)^3

Answer:

(𝑥 + 2)^3 + (𝑥 − 2)^3

According to the equation

𝑎^3 + 𝑏^3 = (𝑎 + 𝑏)(𝑎^2 − 𝑎𝑏 + 𝑏^2)

We get,

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

According to the equation,

(𝑎 + 𝑏)^2 = 𝑎^2 + 2𝑎𝑏 + 𝑏^2

(𝑎 − 𝑏)^2 = 𝑎^2 − 2𝑎𝑏 + 𝑏^2

So we get,

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

= 2𝑥(𝑥^2 + 4𝑥 + 4 − 𝑥^2 + 4 + 𝑥^2 − 4𝑥 + 4)

= 2𝑥(𝑥^2 + 12)

"hi students
welcome to redo learning here i am your
leader tutor
to help you solve the question the
question we have is
x plus 2 whole q plus x minus 2 whole q
now here we will consider x plus 2 as a
aq
and x minus 2 as a b cube
now here we'll apply the formula a plus
b in bracket a square minus
a b plus b square
so we'll write this
x plus 2 plus
x minus 2.
in the second bracket x plus 2
whole square minus
x plus 2 multiplied by
x minus 2 plus x minus 2
whole square now if you simplify the
first part this minus 2 minus will get
cancelled
and the answer will be 2 x
in the second bracket the big bracket
first will write the
x plus 2 whole square x square
plus 4 x plus
4 minus
now if we simplify this to bracket x
plus 2 x minus 2
we can write it as a x square
a square minus b square so x square
minus b
square which is equals to 4.
in the third bracket x square
minus 4x plus
4. now we'll simplify the square
brackets
now for the square bracket we can write
we can see
it's x square
x square x square will get added so it
will be 2
x square plus 4 x and minus 4 x will get
cancelled
then 4x and 4x will further get added so
it's 8
minus x square plus
4. this is in the bracket part
now if we simplify the bracket further
this 8 plus 4 will be 12
and 2x square minus x square will be
x square so it's x square plus 12
so x square plus 12
in bracket in outside the bracket it's
2x now the answer will be 2
x cube plus 24.
so this is the simplified answer that we
get for
this question which is 2 x cube
plus 24.
so what we did we first applied the aq
plus bq formula
the next we applied in the bracket it's
a
square a plus b whole square
and here the bracket a square minus b
square here
a minus b whole square on further
simplification of the bracket
we can see we are getting x square plus
12 and an outside the bracket we are
getting
2x so this way
further simplification give us the
answer 2x cube plus 24.
so i hope you understood the question
for any doubt you can write in the
comment section
for regular updates do subscribe to the
video channel thank you
"

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