Given parameters; 
 The radius of a circle is increased by a factor of x; 
 let the radius of the circle = r; 
 The increased radius = rx 
Area of a circle is given as πr²; 
 Initially, the area of the circle = πr²
where r is the radius
New area after the increase = π x (rx)² = πr²x²
To compare the factor with which the area increased; 
 Factor = 
 = πr²x² / πr² = x²
 = πr²x² / πr² = x²
The area increased by a factor of x²