Question

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

Answer 1

Answer:

$(m + 2)^{2} - m^{2} - 12 = 4(m - 2)$

Step-by-step 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.

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