Question

Prove algebraically that (m + 2)2 – m 2 – 12 is always a multiple of 4

Answer 1

`(m + 2)^(2) - m^(2) - 12 = 4(m - 2)`

Explanation:

Step 1:

Write the expression

`(m+2)^(2) - m^(2) - 12`

Step 2: Expand
`(m + 2)^(2)`

`(m+2)^(2) - m^(2) - 12\\(m+2)(m+2) - m^(2) - 12\\m^(2) + 2m + 2m + 4 - m^(2) - 12`

Step 3: Collect similar terms

`m^(2) - m^(2) + 4m + 4 - 12\\4m - 8`

Step 4: Factor 4 out of the expression to prove that the expression is a multiple of 4.

`Therefore\\4m - 8 = 4(m - 2)\\Hence,\\(m+2)^(2) - m^(2) - 12 is a multiply of 4 because the expression is equal to 4(m-2)`