Question 198380
# 1




{{{(5*sqrt(3)-15*sqrt(5))(4*sqrt(3)+12*sqrt(5))}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(5*sqrt(3))-15*sqrt(5))(highlight(4*sqrt(3))+12*sqrt(5))}}} Multiply the <font color="red">F</font>irst terms:{{{(5*sqrt(3))*(4*sqrt(3))=60}}}.



{{{(highlight(5*sqrt(3))-15*sqrt(5))(4*sqrt(3)+highlight(12*sqrt(5)))}}} Multiply the <font color="red">O</font>uter terms:{{{(5*sqrt(3))*(12*sqrt(5))=60*sqrt(15)}}}.



{{{(5*sqrt(3)+highlight(-15*sqrt(5)))(highlight(4*sqrt(3))+12*sqrt(5))}}} Multiply the <font color="red">I</font>nner terms:{{{(-15*sqrt(5))*(4*sqrt(3))=-60*sqrt(15)}}}.



{{{(5*sqrt(3)+highlight(-15*sqrt(5)))(4*sqrt(3)+highlight(12*sqrt(5)))}}} Multiply the <font color="red">L</font>ast terms:{{{(-15*sqrt(5))*(12*sqrt(5))=-900}}}.



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

So we have the terms: {{{60}}}, {{{60*sqrt(15)}}}, {{{-60*sqrt(15)}}}, {{{-900}}} 



{{{60+60*sqrt(15)-60*sqrt(15)-900}}} Now add every term listed above to make a single expression.



{{{-840}}} Now combine like terms.



So {{{(5*sqrt(3)-15*sqrt(5))(4*sqrt(3)+12*sqrt(5))}}} FOILs to {{{-840}}}.



In other words, {{{(5*sqrt(3)-15*sqrt(5))(4*sqrt(3)+12*sqrt(5))=-840}}}.



<hr>


# 2


{{{root(3,y^4)*root(3,16y^5)}}} Start with the given expression.



{{{root(3,y^4*16y^5)}}} Combine the roots.



{{{root(3,16y^9)}}} Multiply



{{{root(3,8*2*y^9)}}} Factor 16 to get 8*2



{{{root(3,8*2*(y^3)^3)}}} Rewrite {{{y^9}}} as {{{(y^3)^3}}}



{{{root(3,8)*root(3,2)*root(3,(y^3)^3)}}} Break up the root.



{{{2*root(3,2)*root(3,(y^3)^3)}}} Evaluate the cube root of 8 to get 2



{{{2*root(3,2)*y^3}}} Evaluate the cube root of {{{(y^3)^3}}} to get {{{y^3}}}



{{{2y^3*root(3,2)}}} Rearrange the terms.



So {{{root(3,y^4)*root(3,16y^5)=2y^3*root(3,2)}}}