Solution
= Solution
Contracting the <Kronecker delta> identifies $i=k$. The remaining two independent sums are <dot products>, so the <Einstein summation convention> gives
$$
a_i\delta_{ik}b_ma_mc_k
=\left(\sum_k a_kc_k\right)\left(\sum_m b_ma_m\right)
=\boxed{(\mathbf a\cdot\mathbf c)(\mathbf a\cdot\mathbf b)}.
$$
The index expression here is verified against the PDF because the OCR corrupts it completely.