# Thread: 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: $\displaystyle (x+\Delta x)^2= (x+ \Delta x)(x+ \Delta x)= x^2+ (\Delta x)(x)+ x(\Delta x)+ (\Delta x)^2$
$\displaystyle = x^2+ 2x\Delta x+ (\Delta x)^2k$

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

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