Quiz (1 point)
Prove that:
((a ⋅ b) ⋅ 2) + (((a ⋅ a) + ((a ⋅ b) ⋅ (-2))) + (b ⋅ b)) = (a ⋅ a) + (b ⋅ b)
The following properties may be helpful:
- ((a + b) + c) + d = ((a + c) + b) + d
- (a ⋅ 2) + (a ⋅ (-2)) = 0
- (a + b) + c = a + (b + c)
- 0 + a = a
- ((a + b) + c) + d = a + ((b + c) + d)
if the following are true:
- a = b + c
- b = d
then a = d + c
if the following are true:
- a = b
- b = c
then a = c
if a = b, then b = a
if the following are true:
- a = b
- b = c
then a = c
if the following are true:
- a = b
- b = c
then a = c
Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.