Which of these expressions is equivalent to m^2 - n^2 - 14n - 49?

n = m - 7 or n = - m - 7

Step-by-step explanation:

Solve for n:

m^2 - (n + 7) ^2 = 0

The left hand side factors into a product with two terms:

(-7 + m - n) (7 + m + n) = 0

Split into two equations:

-7 + m - n = 0 or 7 + m + n = 0

Subtract m - 7 from both sides:

-n = 7 - m or 7 + m + n = 0

Multiply both sides by - 1:

n = m - 7 or 7 + m + n = 0

Subtract m + 7 from both sides:

Answer: n = m - 7 or n = - m - 7