Simplify (-2+i)(3-6i)

Problem

(−2+i)*(3−6*i)

Solution

1. Apply the FOIL method to multiply the two binomials by distributing each term in the first factor to each term in the second factor.

(−2)*(3)+(−2)*(−6*i)+(i)*(3)+(i)*(−6*i)

2. Perform the multiplication for each individual term.

−6+12*i+3*i−6*i2

3. Combine like terms involving the imaginary unit i

−6+15*i−6*i2

4. Substitute −1 for i2 based on the definition of the imaginary unit.

−6+15*i−6*(−1)

5. Simplify the constant terms by performing the multiplication and then adding the real numbers.

−6+15*i+6

0+15*i

Final Answer

(−2+i)*(3−6*i)=15*i

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