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We study random walks on various group extensions. Under certain bounded generation and bounded scaled conditions, we estimate the spectral gap of a random walk on a quasi-random-by-nilpotent group in terms of the spectral gap of its projection to the quasi-random part. We also estimate the spectral gap of a random-walk on a product of two quasi-random groups in terms of the spectral gap of its projections to the given factors. Based on these results, we estimate the spectral gap of a random walk on the ${\mathbb{F}}_q$-points of a perfect algebraic group $\mathbb{G}$in terms of the spectral gap of its projections to the almost simple factors of the semisimple quotient of $\mathbb{G}$. These results extend a work of Lindenstrauss and Varjú and an earlier work of the authors. Moreover, using a result of Breuillard and Gamburd, we show that there is an infinite set $\mathcal{P}$of primes of density one such that, if $k$is a positive integer and $\mathbb{G}=\mathbb{U}⋊<\#comment/>({\mathrm{SL}}_2{)}_{\mathbb{Q}}^m$is a perfect group and $\mathbb{U}$is a unipotent group, then the family of all the Cayley graphs of $\mathbb{G}\left(\mathbb{Z}/\underset{i=1}{\overset{k}{\prod <\#comment/>}}{p}_i\mathbb{Z}\right)$, $p_i\in <\#comment/>\mathcal{P}$, is a family of expanders.