\( t^{2}-8 t+16 \) can be factorised to give an expression of the form \[ (t+a)^{2} \text {, where } a \text { is an integer. } \] Work out the value of \( a \).

The expression \( t^{2}-8t+16 \) can be recognized as a perfect square trinomial. It can be rewritten in the form \( (t + a)^2 \). To find the value of \( a \), we observe that the middle term \( -8t \) suggests that \( a \) should be negative since the form is \( (t - b)^2 = t^2 - 2bt + b^2 \). Here, \( 2b = 8 \), which gives \( b = 4 \). Thus, our expression factors as \( (t - 4)^2 \). From this, we can see that \( a = -4 \).