## Algebra 2 Common Core

$13-6i$
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $(2+i)(4-5i) ,$ is equivalent to \begin{align*} & 2(4)+2(-5i)+i(4)+i(-5i) \\&= 8-10i+4i-5i^2 \\&= 8-10i+4i-5(-1) &\text{ (use $i^2=-1$)} \\&= 8-10i+4i+5 .\end{align*} Combining the real parts and the imaginary parts, the expression above is equivalent to \begin{align*} & (8+5)+(-10i+4i) \\&= 13+(-6i) \\&= 13-6i .\end{align*} Hence, the simplified form of the given expression is $13-6i$.