Simplify 9a^3b^2c-5a^2bc^2-12a^3b^2c+3a^2bc^2+4a^3b^2c

$9 a^{3} b^{2} c - 5 a^{2} b c^{2} - 12 a^{3} b^{2} c + 3 a^{2} b c^{2} + 4 a^{3} b^{2} c$

Subtract $12 a^{3} b^{2} c$ from $9 a^{3} b^{2} c$ .

$- 3 a^{3} b^{2} c - 5 a^{2} b c^{2} + 3 a^{2} b c^{2} + 4 a^{3} b^{2} c$

Add $- 3 a^{3} b^{2} c$ and $4 a^{3} b^{2} c$ .

$1 a^{3} b^{2} c - 5 a^{2} b c^{2} + 3 a^{2} b c^{2}$

Multiply $a^{3}$ by $1$ .

$a^{3} b^{2} c - 5 a^{2} b c^{2} + 3 a^{2} b c^{2}$

Add $- 5 a^{2} b c^{2}$ and $3 a^{2} b c^{2}$ .

$a^{3} b^{2} c - 2 a^{2} b c^{2}$