Question

`(12t^6-8t^8)÷(2t^3)`? Divide

Answer 1

See a solution process below:

Explanation:

We can rewrite the expression as:

`(12t^6 - 8t^8)/(2t^3)`

This can be rewritten as:

`(12t^6)/(2t^3) - (8t^8)/(2t^3) =>`

`(6t^6)/t^3 - (4t^8)/t^3`

We can then use this rule of exponents to divide the `t` terms:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`(6t^color(red)(6))/t^color(blue)(3) - (4t^color(red)(8))/t^color(blue)(3) =>`

`6t^(color(red)(6)-color(blue)(3)) - 4t^(color(red)(8)-color(blue)(3)) =>`

`6t^3 - 4t^5`

However, because we cannot divide by `0` the solution is:

`(12t^6 - 8t^8) -: (2t^3) => 6t^3 - 4t^5` Where `t != 0`

Answer 2

`6t^3-4t^5`

Explanation:

`"factorise the numerator and cancel "color(blue)"common factors"`

`"take out a "color(blue)"common factor "4t^6`

`=4t^6(3-2t^2)`

`rArr(4t^6(3-2t^2))/(2t^3)tot!=0`

`=(cancel(4)^2cancel(t^6)t^3(3-2t^2))/(cancel(2)cancel(t^3)`

`=2t^3(3-2t^2)=6t^3-4t^5`

Answer 3

`2t^3(3-2t^2)` but `t!=0`

Explanation:

Given: `(12t^6-8t^8)/(2t^3)`

Write as:

`color(white)("ddd")[(12t^6)/(2t^3)]color(white)("ddddd")-color(white)("dddd")[(8t^8)/(2t^3)]`

`[(2xx6xxt^3xxt^3)/(2xxt^3)]color(white)("d")-[(2xx4xxt^3xxt^5)/(2xxt^3)]`

`[2/2xx6xxt^3/t^3xxt^3]-[2/2xx4xxt^3/t^3xxt^5]`

`color(white)("d")[1xx6xx1xxt^3]color(white)(".d")-color(white)("d")[1xx4xx1xxt^5]`

`[6t^3]-[4t^5]`

`[2xx3xxt^3]-[2xx2xxt^3xxt^2]`

Factor out `2t^3`

`2t^3(3-2t^2)`
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Note that this is the same as: `6t^3-4t^5`

However, mathematically it is 'not allowed' to divide by 0. We call this condition 'undefined'.

Given that we have `(12t^6-8t^8)/(2t^3)` then `2t^3!=0 => t!=0`