Algebraic Manipulation Given that 
$ a^2 - b^2 = 60 $ 
and
$a - b = 6 $
$a + b = 10$
Find value of $a\cdot b$
I tried 
$(a-b)^2 = 6^2 \longrightarrow a^2 - 2ab + b^2 = 36$

We can arrange the equations as a system of equations as follows
$$\begin{cases} a-b=6\\ a+b=10 \end{cases}$$
Now we can add the two equations 
$$(a-b)+(a+b)=6+10$$
$$ 2a=16 \rightarrow a=8 $$
$$ a-b=6,\ 8-b=6\rightarrow b=2 $$
So the solutions are $a=8$ and $b=2$
