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.

1. Is *x*^{2} - 6*x* + 13 an identity of (*x* - 3)^{2} + 4?

Answer: Yes

Expand (*x* - 3)^{2} + 4 to *x*^{2} - 6*x* + 13. Both expressions are now identical, so they are an identity.

2. Show that (*x* + *ay*)^{2} + (*x* - *ay*)^{2} = 2(*x*^{2} + *a*^{2}*y*^{2})

Answer: Expand (*x* + *ay*)^{2} + (*x* - *ay*)^{2}

= *x*^{2} + 2*ay* + *a*^{2}*y*^{2} + *x*^{2} - 2*ay* + *a*^{2}*y*^{2}

= 2*x*^{2} + 2*a*^{2}*y*^{2}

= 2(*x*^{2} + *a*^{2}*y*^{2})

Our iOS app has over 1,000 questions to help you practice this and many other topics.

Available to download free on the App Store.

Available to download free on the App Store.