In a rectangle model with sides (x-2) and (x+6) what will be the constant part?

(-12)

The constant part of a product comes from multiplying the terms that do not contain the variable. The rectangle has sides \\(x-2\\) and \\(x+6\\). Its area is \\( (x-2)(x+6)\\). The constant terms are \\(-2\\) and \\(6\\), so their product is \\((-2)(6)=-12\\). Therefore, the constant part is \\(-12\\), and option B is correct. The negative sign is essential because the first side contains \\(-2\\), not \\(2\\).

For a complete check, distribute the factors: \\(x\cdot x=x^2\\), \\(x\cdot6=6x\\), \\((-2)\cdot x=-2x\\), and \\((-2)\cdot6=-12\\). Thus the full product is \\(x^2+4x-12\\), whose constant term is indeed \\(-12\\). Option A would result from incorrectly treating \\(-2\\) as positive. Options C and D do not come from multiplying the two constant terms. In an area model, the bottom-right constant rectangle has signed area \\(-12\\), so its sign must be retained.

This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.