a)(c-2)(c+3)-(c-1)^2

Expand the terms: $$(c^2 + 3c - 2c - 6) - (c^2 - 2c + 1)$$. Simplify: $$(c^2 + c - 6) - (c^2 - 2c + 1)$$. Distribute the negative sign: $$c^2 + c - 6 - c^2 + 2c - 1$$. Combine like terms: $$(c^2 - c^2) + (c + 2c) + (-6 - 1)$$. The result is $$3c - 7$$.