Question

Regina says (m+n)² is equivalent to m²+n², but Henry disagrees. Who is correct? Convince the person who is wrong why s/he is wrong and explain what is true.

Answer 1

Hello from MrBillDoesMath

Answer: Henry is correct.

Discussion:

Consider this example, m = 3, n = -3. Then

(m+n)^2 = ( 3 -3)^2 = 0^2 = 0 and

m^2 + n^2 = (3)^2 + (-3)^2 = 9 + 9 = 18 which is not equal to 0.

In general (m + n)^2 = m^2 + 2mn + n^2 = m^2 + n^2 + 2mn

Note the highlighted term (2mn) above. That is why Regina's statement fails to be true

Thank you,

Mr. B