$(i^{3} + 2) (i - 2) (i^{2} - 3) = - 16 i + 12$

Explanation

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$(i^{3} + 2) (i - 2) (i^{2} - 3) \overset{◯}{1} (- i + 2) (i - 2) \cdot (- 1 - 3) \overset{◯}{2} (- i + 2) (i - 2) \cdot (- 4) \overset{◯}{3} (- i^{2} + 2 i + 2 i - 4) \cdot (- 4) \overset{◯}{4} (- i^{2} + 4 i - 4) \cdot (- 4) \overset{◯}{5} (1 + 4 i - 4) \cdot (- 4) \overset{◯}{6} (4 i - 3) \cdot (- 4) \overset{◯}{7} - 16 i + 12$
①	$i^{3} = i^{2} \cdot i = (- 1) \cdot i = - i$ $i^{2} = - 1$
②	Combine like terms: $- 1 - 3 = - 4$
③	Multiply each term of $(- i + 2)$ by each term in $(i - 2)$ . $(- i + 2) \cdot (i - 2) = - i^{2} + 2 i + 2 i - 4$
④	Combine like terms: $- i^{2} + 2 i + 2 i - 4 = - i^{2} + 4 i - 4$
⑤	$- i^{2} = - (- 1) = 1$
⑥	Combine like terms: $1 + 4 i - 4 = 4 i - 3$
⑦	$(4 i - 3) \cdot - 4 = - 16 i + 12$

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(i3+2)(i−2)(i2−3)=−16i+12

$(i^{3} + 2) (i - 2) (i^{2} - 3) = - 16 i + 12$