SOLUTION: I have a couple...i just dont get this stuff! (x^3+2x+1)(2x^2-4x-5) and (x-2)(x+7)(2x+3)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have a couple...i just dont get this stuff! (x^3+2x+1)(2x^2-4x-5) and (x-2)(x+7)(2x+3)       Log On


   

Question 118881: I have a couple...i just dont get this stuff!
(x^3+2x+1)(2x^2-4x-5)
and
(x-2)(x+7)(2x+3)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1




%28x%5E3%2B2x%2B1%29%282x%5E2-4x-5%29 Start with the given expression



x%5E3%282x%5E2-4x-5%29%2B2x%282x%5E2-4x-5%29%2B1%282x%5E2-4x-5%29 Expand the expression. Remember for something like %28a%2Bb%2Bc%29%28d%2Be%2Bf%29 it expands to a%28d%2Be%2Bf%29%2Bb%28d%2Be%2Bf%29%2Bc%28d%2Be%2Bf%29


Distribute


2x%5E5-4x%5E4-5x%5E3%2B4x%5E3-8x%5E2-10x%2B2x%5E2-4x-5 Multiply


-4x%5E4-6x%5E2-x%5E3-14x%2B2x%5E5-5 Combine like terms



2x%5E5-4x%5E4-x%5E3-6x%5E2-14x-5 Now rearrange the terms in descending order


So %28x%5E3%2B2x%2B1%29%282x%5E2-4x-5%29 expands and simplifies to 2x%5E5-4x%5E4-x%5E3-6x%5E2-14x-5.

In other words, %28x%5E3%2B2x%2B1%29%282x%5E2-4x-5%29=2x%5E5-4x%5E4-x%5E3-6x%5E2-14x-5




If you need more help with multiplying polynomials, check out this Long Multiplication Calculator







#2


%28x-2%29%28x%2B7%29%282x%2B3%29 Start with the given expression

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First let's foil %28x-2%29%28x%2B7%29




%28x-2%29%28x%2B7%29 Start with the given expression



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


%28highlight%28x%29-2%29%28highlight%28x%29%2B7%29 Multiply the First terms:%28x%29%2A%28x%29=x%5E2


%28highlight%28x%29-2%29%28x%2Bhighlight%287%29%29 Multiply the Outer terms:%28x%29%2A%287%29=7x


%28x%2Bhighlight%28-2%29%29%28highlight%28x%29%2B7%29 Multiply the Inner terms:%28-2%29%2A%28x%29=-2x


%28x%2Bhighlight%28-2%29%29%28x%2Bhighlight%287%29%29 Multiply the Last terms:%28-2%29%2A%287%29=-14


x%5E2%2B7x-2x-14 Now collect every term to make a single expression



x%5E2%2B5x-14 Now combine like terms



So %28x-2%29%28x%2B7%29 foils and simplifies to x%5E2%2B5x-14



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


So our expression then becomes


%28x%5E2%2B5x-14%29%282x%2B3%29





Now let's multiply out %28x%5E2%2B5x-14%29%282x%2B3%29

%28x%5E2%2B5x-14%29%282x%2B3%29 Start with the given expression



x%5E2%282x%2B3%29%2B5x%282x%2B3%29-14%282x%2B3%29 Expand the expression. Remember for something like %28a%2Bb%2Bc%29%28d%2Be%29 it expands to a%28d%2Be%29%2Bb%28d%2Be%29%2Bc%28d%2Be%29


Distribute


2x%5E3%2B3x%5E2%2B10x%5E2%2B15x-28x-42 Multiply


13x%5E2%2B2x%5E3-13x-42 Combine like terms



2x%5E3%2B13x%5E2-13x-42 Now rearrange the terms in descending order


So %28x-2%29%28x%2B7%29%282x%2B3%29 expands and simplifies to 2x%5E3%2B13x%5E2-13x-42.

In other words, %28x-2%29%28x%2B7%29%282x%2B3%29=2x%5E3%2B13x%5E2-13x-42




If you need more help with multiplying polynomials, check out this Long Multiplication Calculator