We have to prove: (2x-1)^2-(x-3)^2 = (3x-4)(x+2)

Take the left hand side

(2x-1)^2-(x-3)^2

Use the relation x^2 - y^2 = (x - y)(x + y)

=> (2x - 1 - x + 3)(2x - 1 + x - 3)

=> (x + 2)(3x - 4)

which is the right hand side.

**This proves that (2x-1)^2-(x-3)^2 = (3x-4)(x+2)**