Question

How do you factor:
1. e^(2x) + 2 + e^(-2x)
2. cos²x + 6cosx + 8
3. 1-sin²x

Answer 1

from the bottom up
\(1-a^2=(1-a)(1+a)\) so \(1-\sin^2(x)=(1-\sin(x))(1+\sin(x))\)

Answer 2

\(x^2+6x+8=(x+2)(x+8)\) so \(\cos^2(x)+6\cos(x)+8=(\cos(x)+2)(\cos(x)+8)\)

Answer 3

and finally the tricky one
\[(x+\frac{1}{x})^2=x^2+2+\frac{1}{x^2}\] so
\[e^{2x}+2+e^{-2x}=(e^x+e^{-x})^2\]