```Question 192031

Now let's FOIL the expression.

Remember, when you FOIL an expression, you follow this procedure:

{{{(highlight(3)+sqrt(-5))(highlight(7)-sqrt(-10))}}} Multiply the <font color="red">F</font>irst terms:{{{(3)*(7)=21}}}.

{{{(highlight(3)+sqrt(-5))(7+highlight(-sqrt(-10)))}}} Multiply the <font color="red">O</font>uter terms:{{{(3)*(-sqrt(-10))=-3*sqrt(-10)=-3i*sqrt(10)}}}.

{{{(3+highlight(sqrt(-5)))(highlight(7)-sqrt(-10))}}} Multiply the <font color="red">I</font>nner terms:{{{(sqrt(-5))*(7)=7*sqrt(-5)=7i*sqrt(5)}}}.

{{{(3+highlight(sqrt(-5)))(7+highlight(-sqrt(-10)))}}} Multiply the <font color="red">L</font>ast terms:{{{(sqrt(-5))*(-sqrt(-10))=5*sqrt(2)}}}.

---------------------------------------------------

So we have the terms: {{{21}}}, {{{-3i*sqrt(10)}}}, {{{7i*sqrt(5)}}}, {{{5*sqrt(2)}}}

{{{21-3i*sqrt(10)+7i*sqrt(5)+5*sqrt(2)}}} Now add every term listed above to make a single expression.

{{{21+5*sqrt(2)+7i*sqrt(5)-3i*sqrt(10)}}} Rearrange the terms

{{{(21+5*sqrt(2))+(7*sqrt(5)-3*sqrt(10))*i}}} Group the terms and factor out the term "i"

So {{{(3+sqrt(-5))(7-sqrt(-10))}}} FOILs to {{{(21+5*sqrt(2))+(7*sqrt(5)-3*sqrt(10))*i}}}.

In other words, {{{(3+sqrt(-5))(7-sqrt(-10))=(21+5*sqrt(2))+(7*sqrt(5)-3*sqrt(10))*i}}}.

The number is now in standard form {{{a+bi}}} where {{{a=21+5*sqrt(2)}}} and {{{b=7*sqrt(5)-3*sqrt(10)}}}
```