Question

What is the factored form of eight x cubed plus twenty seven

Answer 1

eight x cubed plus twenty seven in mathematical notation is
`8x^(3)+27`. Notice that the second term, 27, can be expressed as a cube:
`27=3*3*3=3^(3)`. 8 can aslo be expressed as a cube:
`8=2*2*2=2^3` so we can rewrite our expression as a sum of two cubes cubes:

`8x^3+27=(2x)^3+3^3`
Now, to factor our sum of cubes, we are going to use the formula:
`a^3+b^3=(a+b)(a^2-ab+b^2)`. From our previous calculations we can infer that
`a=2x`, and
`b=3`, so lets replace those values in our formula:

`a^3+b^3=(a+b)(a^2-ab+b^2)`

`8x^3+3^3=(2x+3)((2x)^2-6x+3^2)`

`8x^3+3^3=(2x+3)(4x^2-6x+9)`

We can conclude that the factored form of eight x cubed plus twenty seven is
`(2x+3)(4x^2-6x+9)`.