Question 27810
1) Factor:
{{{64-(r+2t)^2}}} You should recognise this as the difference of two squares: {{{64 = 8^2}}} and {{{(r+2t)^2}}}
 The difference of two squares can be factored:
{{{A^2 - B^2 = (A+B)(A-B)}}} Appplying this to your problem:

{{{8^2 - (r+2t)^2 = (8 + (r+2t))(8 - (r+2t))}}} = {{{(8+r+2t)(8-r-2t)}}}

2) Factor:
{{{-k^2-h^2+2kh+4}}} If you rearrange this expression, you will see that it is really the difference of two squares.

{{{4 - (k^2-2kh+h^2)}}} Factor the parentheses.
{{{4 - (k-h)^2}}} Now it's in the form of: {{{A^2 - b^2}}}which will factor nicely.

{{{4 - (k-h)^2 = (2 + (k-h))(2 - (k-h))}}} = {{{(2+k-h)(2-k+h)}}}

You can verify these answers by multiplying the factors to see that you get back the original expressions.
I'll leave this as an exercise for the student!