Question 161477
{{{(5y^2w^2+z)(2y^3w^2+3z)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(5y^2w^2)+z)(highlight(2y^3w^2)+3z)}}} Multiply the <font color="red">F</font>irst terms:{{{(5y^2w^2)(2y^3w^2)=(5*2)(y^2*y^3)(w^2*w^2)=10y^(2+3)w^(2+2)=10y^5w^4}}}.



{{{(highlight(5y^2w^2)+z)(2y^3w^2+highlight(3z))}}} Multiply the <font color="red">O</font>uter terms:{{{(5y^2w^2)(3z)=(5*3)y^2w^2z=15y^2w^2z}}}.



{{{(5y^2w^2+highlight(z))(highlight(2y^3w^2)+3z)}}} Multiply the <font color="red">I</font>nner terms:{{{(z)(2y^3w^2)=2y^3w^2z}}}.



{{{(5y^2w^2+highlight(z))(2y^3w^2+highlight(3z))}}} Multiply the <font color="red">L</font>ast terms:{{{(z)(3z)=3z^2}}}.



{{{10y^5w^4+15y^2w^2z+2y^3w^2z+3z^2}}} Now collect every term to make a single expression.



So {{{(5y^2w^2+z)(2y^3w^2+3z)}}} FOILs to {{{10y^5w^4+15y^2w^2z+2y^3w^2z+3z^2}}}.



In other words, {{{(5y^2w^2+z)(2y^3w^2+3z)=10y^5w^4+15y^2w^2z+2y^3w^2z+3z^2}}}.