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.

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

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

Answer: Yes

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})

See also Vocabulary

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