## Answers to exercises

##### Exercise 1

\(x+y\)

##### Exercise 2

\(x^n-1\)

##### Exercise 3

Both sides equal \(a^2b+a^2c+ab^2+2abc+b^2c+ac^2+bc^2\).

##### Exercise 4

\((4x^2-1)(x-3)\); \(x=\pm \frac{1}{2}\), \(x=3\)

##### Exercise 5

\((a-b)(a+b)^3\)

##### Exercise 6

\(\dfrac{-13x}{(x + 1)(x + 2)(x + 3)}\)

##### Exercise 7

\(x=2\)

##### Exercise 8

\((x-1)^2+(y-3)^2=11\), centre \((1,3)\), radius \(\sqrt{11}\).

##### Exercise 9

\(x=2\), \(y=4\) or \(x=-1\), \(y=1\).

##### Exercise 10

\(n= \dfrac{\log(\frac{A}{P})}{\log(1+R)}\)