Question

Which of the equations are true identities?

A. m^3-1= (m - 1) (1 + m + m²)
B. (n + 3)^2 + 2n = 8n + 13

Answer 1

Equation A is true; Equation B is not

Explanation:

There is a standard formula for the "difference of cubes" that is:

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

and this perfectly matches equation A.

Equation B has the square of n (n^2) on the left side but not on the right side. Thus this is not an identity.