Question

Write a polynomial expression for (delta)V, the change in the volume of a cube as the length of its side increases by one unit.

Answer 1

if you call the side \(x\) then \(V(x)=x^3\) and so \(V(x+1)=(x+1)^2\)
the change would be
\[\Delta V=(x+1)^2-x^2\]which can be simplified by cubing

Answer 2

\[(x+1)^3-x^3=x^3+3x^2+3x+1-x^3=3x^2+3x+1\]

Answer 3

That was beautiful! Thank you!!!!

Answer 4

yw