N is a multiple of 5 A = N + 1
B = N – 1
Prove, using algebra, that A2 – B2 is always a multiple of 20

Proved

Step-by-step explanation:

Given

Required

Prove that is a multiple of 20

First, we need to evaluate

Start by applying difference of two squares

Substitute values for A and B

Collect Like Terms

Since, N is a multiple of 5, then the possible values of N are:

For each of these values, the possible values of are

The above shows that is a multiple of 20

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)