(b+c)(b-c)

To simplify this expression, we will use the FOIL method, which stands for First, Outer, Inner, Last.

First, we multiply the first terms of each binomial:

b * b = b^2

Next, we multiply the outer terms:

b * -c = -bc

Then, we multiply the inner terms:

c * b = cb

Lastly, we multiply the last terms:

c * -c = -c^2

Now, we can combine the like terms:

(b^2) + (-bc) + (cb) + (-c^2)

Simplifying further, we have:

b^2 - bc + cb - c^2

Since -bc and cb represent the same terms but with opposite signs, we can combine them:

b^2 - 2bc - c^2

Therefore, the simplified expression is b^2 - 2bc - c^2.