# How do you rewrite (sin x - cos x)(sin x + cos x)? Thank you.

##### 2 Answers

#### Explanation:

You're probably used to dealing with this only in quadratics, but the expression is in the **difference of squares** pattern

where

We can just plug in our values for

Which can be rewritten as

If you don't believe me, we can **FOIL** this expression to make sure:

With FOIL, we multiply the first, outside, inside and last terms and add the result. Thus, we have:

- First terms:
#sinx*sinx=color(red)(sinx^2)# - Outside terms:
#sinx*cosx=sinxcosx# - Inside terms:
#sinx*-cosx=-sinxcosx# - Last terms:
#-cosx*cosx=-color(blue)(cosx^2)#

Now we have

The middle terms obviously cancel out, and we can rewrite this as

The key realization is that the original expression in question was in a difference of squares pattern.

If you have a

Hope this helps!

#### Explanation:

Reminder of trig identity:

Finally,