An object is reduced or enlarged uniformly in all dimensions. The print shown is a watercolour painting called August Chinook by Gena LaCoste of Medicine Hat, Alberta. This print is going to be enlarged by a factor of $3.$ The side length of the original can be represented by $(2x-3)cm.$

a$)$ Use your understanding of differences of squares to write an expression that represents the difference in the areas of the original print and the enlargement.

b$)$ Multiply this expression to write it in the form $a{x}^2+bx+c.$

c$)$ Verify that your expressions in parts a$)$ and b$)$ are correct by substituting a value for $x.$