An identity is an expression written in another form. Although it may look like an equation, attempting to solve the equation results in a solution of x = x, or similar.
1. Is x2 - 6x + 13 an identity of (x - 3)2 + 4?
Expand (x - 3)2 + 4 to x2 - 6x + 13. Both expressions are now identical, so they are an identity.
2. Show that (x + ay)2 + (x - ay)2 = 2(x2 + a2y2)
Answer: Expand (x + ay)2 + (x - ay)2
= x2 + 2ay + a2y2 + x2 - 2ay + a2y2
= 2x2 + 2a2y2
= 2(x2 + a2y2)