Malonic acid on reaction with ${\mathrm{P}}_4{\mathrm{O}}_{10}$ gives :

Malonic acid produces an oxide when it is dehydrated with  ${\mathrm{P}}_4{\mathrm{O}}_{10}$ When malonic acid reacts with  phosphorus pentoxide, it produces pyrophosphoric acid and tricarbon dioxide.

$2{\mathrm{CH}}_2{\left(\mathrm{COOH}\right)}_2+{\mathrm{P}}_4{\mathrm{O}}_{10}\to 2{\mathrm{H}}_4{\mathrm{P}}_2{\mathrm{O}}_7+2{\mathrm{C}}_3{\mathrm{O}}_2$