Prove algebraically that the sum of the squares of two consecutive multiples of 5 is not a multiple of 10.

First let’s break this statement down. At the core of this sentence are two consecutive multiples of 5. How can we represent these using algebra? Let’s use 5a where “a” is an integer. A consecutive multiple of 5 would then be 5(a + 1). Use an example for “a” to understand this.Then, the SUM of the SQUARES refers precisely to the following:(5a)^2 + (5(a+1))^2which when expanded, becomes50a^2 + 10a + 25 Under evaluation, the first 2 terms will always be multiples of 10, but adding 25 stops the entire expression from being a multiple of 10.