Equations and Identities

Equations and Identities

GCSE(F) GCSE(H)

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.

Examples

1. Is x2 - 6x + 13 an identity of (x - 3)2 + 4?

Answer: Yes

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)