Answer:
[tex]abc\left(a+b+c\right)[/tex] is the required answer.
Step-by-step explanation:
[tex]a^2bc+ab^2c+abc^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\\\=aabc+abbc+abcc\\\\=bac\left(a+b+c\right)[/tex]
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