$\displaystyle (x+1/2)^2 - (x+3/2)^2$
How does it simplify... Is there a name for term of this nature? I've forgotten.
$\displaystyle (x+1/2)^2 - (x+3/2)^2$
= $\displaystyle {(x^2)+2*x*\frac{1}{2}+[\frac{1}{2}]^2} - [(x^2)+2*x*[\frac{3}{2}]+[\frac{3}{2}]^2]$
= $\displaystyle {x^2}+x+\frac{1}{4}-{x^2}-3x-\frac{9}{4}$
= $\displaystyle -2x-\frac{8}{4}$
=$\displaystyle -2x-2$
=$\displaystyle -2(x+1)$