SOLUTION: (5y^2w^2+z)(2y^3 w^2+3z) I tried to use the foil method but I got lost

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Question 161476: (5y^2w^2+z)(2y^3 w^2+3z)
I tried to use the foil method but I got lost
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%285y%5E2w%5E2%2Bz%29%282y%5E3w%5E2%2B3z%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%285y%5E2w%5E2%29%2Bz%29%28highlight%282y%5E3w%5E2%29%2B3z%29 Multiply the First terms:%285y%5E2w%5E2%29%282y%5E3w%5E2%29=%285%2A2%29%28y%5E2%2Ay%5E3%29%28w%5E2%2Aw%5E2%29=10y%5E%282%2B3%29w%5E%282%2B2%29=10y%5E5w%5E4.


%28highlight%285y%5E2w%5E2%29%2Bz%29%282y%5E3w%5E2%2Bhighlight%283z%29%29 Multiply the Outer terms:%285y%5E2w%5E2%29%283z%29=%285%2A3%29y%5E2w%5E2z=15y%5E2w%5E2z.


%285y%5E2w%5E2%2Bhighlight%28z%29%29%28highlight%282y%5E3w%5E2%29%2B3z%29 Multiply the Inner terms:%28z%29%282y%5E3w%5E2%29=2y%5E3w%5E2z.


%285y%5E2w%5E2%2Bhighlight%28z%29%29%282y%5E3w%5E2%2Bhighlight%283z%29%29 Multiply the Last terms:%28z%29%283z%29=3z%5E2.


10y%5E5w%5E4%2B15y%5E2w%5E2z%2B2y%5E3w%5E2z%2B3z%5E2 Now collect every term to make a single expression.


So %285y%5E2w%5E2%2Bz%29%282y%5E3w%5E2%2B3z%29 FOILs to 10y%5E5w%5E4%2B15y%5E2w%5E2z%2B2y%5E3w%5E2z%2B3z%5E2.


In other words, %285y%5E2w%5E2%2Bz%29%282y%5E3w%5E2%2B3z%29=10y%5E5w%5E4%2B15y%5E2w%5E2z%2B2y%5E3w%5E2z%2B3z%5E2.