If a2 − b2 = 36 and a + b = 4, then (a − b) 2 =__________.(a) 36 (b) 9(c) 81 (d) 144

To solve this problem, we can use the given equations and algebraic manipulation.

1. Start with the equation a^2 - b^2 = 36.
2. Notice that this equation can be factored as (a + b)(a - b) = 36.
3. We are also given that a + b = 4.
4. Substitute this value into the factored equation: (4)(a - b) = 36.
5. Simplify the equation: 4a - 4b = 36.
6. Divide both sides of the equation by 4: a - b = 9.
7. Now, we need to find (a - b)^2.
8. Square both sides of the equation: (a - b)^2 = 9^2.
9. Simplify the equation: (a - b)^2 = 81.

Therefore, the answer is (c) 81.