# Math Help - factoring cubed function

1. ## factoring cubed function

(x+(DELTAX))^3

i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help

2. Originally Posted by maybnxtseasn
(x+(DELTAX))^3

i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
It is factored. Do you mean you want to multiply it?

One way: $(x+\Delta x)^2= (x+ \Delta x)(x+ \Delta x)= x^2+ (\Delta x)(x)+ x(\Delta x)+ (\Delta x)^2$
$= x^2+ 2x\Delta x+ (\Delta x)^2k$

and then $(x+ \Delta x)^3= (x+ \Delta x)(x+ \Delta x)^2$ $= (x+ \Delta x)(x^2+ 2x\Delta x+ (\Delta x)^2)$ $= x(x^2)+ \Delta x(x^2)+ x(2x\Delta x)+ \Delta x(2x\Delta x)+ x(\Delta x)^2+ \Delta x(\Delta x)^2$
$= x^2+ 3x^2\Delta x+ 3x(\Delta x)^2+ (\Delta x)^3$

Quicker way: if you know the general formula $(a+ b)^3= a^3+ 3a^2b+ 3ab^2+ b^3$, use that with a= x and $b= \Delta x$ to get the same thing.