Simplify each expression by collecting and combining like terms.
$a^{3} + 2 a^{2} + 3 a^{3} + a^{2} + a^{2}$

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Solution

Simplifying the polynomial
Given, $a^{3} + 2 a^{2} + 3 a^{3} + a^{2} + a^{2}$
Rearrange the like terms and adding them with using distributive law.
$= a^{3} + 2 a^{2} + 3 a^{3} + a^{2} + a^{2} = a^{3} + 3 a^{3} + 2 a^{2} + a^{2} + a^{2} = (1 + 3) a^{3} + (2 + 1 + 1) a^{2} = 4 a^{3} + 4 a^{2}$
Hence, the simplification of $a^{3} + 2 a^{2} + 3 a^{3} + a^{2} + a^{2}$ is $4 a^{3} + 4 a^{2}$ .

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