eight x cubed plus twenty seven in mathematical notation is [tex]8x^{3}+27[/tex]. Notice that the second term, 27, can be expressed as a cube: [tex]27=3*3*3=3^{3}[/tex]. 8 can aslo be expressed as a cube: [tex]8=2*2*2=2^3[/tex] so we can rewrite our expression as a sum of two cubes cubes:
[tex]8x^3+27=(2x)^3+3^3[/tex]
Now, to factor our sum of cubes, we are going to use the formula: [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]. From our previous calculations we can infer that [tex]a=2x[/tex], and [tex]b=3[/tex], so lets replace those values in our formula:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]8x^3+3^3=(2x+3)((2x)^2-6x+3^2) [/tex]
[tex]8x^3+3^3=(2x+3)(4x^2-6x+9)[/tex]
We can conclude that the factored form of eight x cubed plus twenty seven is [tex](2x+3)(4x^2-6x+9)[/tex].
