SOLUTION: Express as a polynomial (2x+10y)^3

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Question 24457: Express as a polynomial
(2x+10y)^3
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Express as a polynomial 
(2x+10y)^3

(2x + 10y)3

This can be done by the binomial theorem.  If that is the
way you were told to do it, post again.  I will only show 
you the basic method, which gives the same answer.

Write the cube as multiplication three times

(2x + 10y)(2x + 10y)(2x + 10y)

Use FOIL to multiply out the second and third parentheses:

(2x + 10y)(4x2 + 20xy + 20xy + 100y2)

Collect terms in the second parentheses

(2x + 10y)(4x2 + 40xy + 100y2)

Use the distributive principle to multiply the two terms
in the first parentheses by the trinomial in the second 
parentheses.

2x(4x2 + 40xy + 100y2) + 10y(4x2 + 40xy + 100y2)

then distribute each:

   8x3 + 80x2y + 200xy2 + 40x2y + 400xy2 + 1000y3

Collect like terms:

  8x3 + 120x2y + 600xy2 + 1000y3

Edwin
AnlytcPhil@aol.com
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