SOLUTION: what is the product of the expression (4w^2-5)(w+5)?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: what is the product of the expression (4w^2-5)(w+5)?      Log On


   

Question 629066: what is the product of the expression (4w^2-5)(w+5)?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%284w%5E2-5%29%28w%2B5%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%284w%5E2%29-5%29%28highlight%28w%29%2B5%29 Multiply the First terms:%284%2Aw%5E2%29%2A%28w%29=4%2Aw%5E3.


%28highlight%284w%5E2%29-5%29%28w%2Bhighlight%285%29%29 Multiply the Outer terms:%284%2Aw%5E2%29%2A%285%29=20%2Aw%5E2.


%284w%5E2%2Bhighlight%28-5%29%29%28highlight%28w%29%2B5%29 Multiply the Inner terms:%28-5%29%2A%28w%29=-5%2Aw.


%284w%5E2%2Bhighlight%28-5%29%29%28w%2Bhighlight%285%29%29 Multiply the Last terms:%28-5%29%2A%285%29=-25.


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So we have the terms: 4%2Aw%5E3, 20%2Aw%5E2, -5%2Aw, -25


4%2Aw%5E3%2B20%2Aw%5E2-5%2Aw-25 Now add every term listed above to make a single expression.


4w%5E3%2B20w%5E2-5w-25 Now combine like terms.


So %284w%5E2-5%29%28w%2B5%29 FOILs to 4w%5E3%2B20w%5E2-5w-25.


In other words, %284w%5E2-5%29%28w%2B5%29=4w%5E3%2B20w%5E2-5w-25.

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