Question

Which expression
is equivalent to 64y18-1000z6

Answer 1

64y^18 -1000z^6 = (4y^6)^3 -(10z^2)^3

Answer 2

`64y^(18) - 1000z^(6) = (4y^(6) )^3 - (10z^2)^3` =
`(4y^6 - 10z^2) (16y^(12) + 40y^6z^2 +100z^4)`

Explanation:

The given expression is
`64y^(18) -1000z^(6)`

Here we can rewrite the given expression.

64 can be written as 4*4*4 =
`4^(3)`

`y^(18) =( y^(6)) ^3` using the power of power rule of exponent.

So.
`64y^(18) = (4y^6)^(3)`

Now we can write 1000
`z^(6)` =
`(10z^2)^3`

Therefore,
`64y^(18) - 1000z^(6) = (4y^(6) )^3 - (10z^2)^3`

This can be written as using the formula
`(a - b)^3 = (a - b)(a^2 + ab + b^2)`

Here a = 4y^6 and b = 10z^2

=
`(4y^6 - 10z^2) (16y^(12) + 40y^6z^2 +100z^4)`