Why do these reactions occur?
Abstraction of $\ce{H+}$ by strong base $\ce{NH2^-}$
$$\ce{CH3-COO- + NH2^- -&gt; ^-CH2-COO- + NH3}$$

Carboxylation to form malonate
$$\ce{^-CH2-COO- + CO2 -&gt; ^-OOC-CH2-COO-}$$

Free malonic acid
$$\ce{^-OOC-CH2-COO- + 2 H+ -&gt; HOOC-CH2-COOH}$$

Dehydration of malonic acid with $\ce{P4O10}$ yields carbon suboxide (unbalanced)
$$\ce{HOOC-CH2-COOH + P4O10-&gt; O=C=C=C=O + H3PO4}$$