SOLUTION: Multiply. {{{(5x+7)(x^3-x+7)}}} Trying to understand these can you show me how this is done through each step. thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Multiply. {{{(5x+7)(x^3-x+7)}}} Trying to understand these can you show me how this is done through each step. thank you.      Log On


   

Question 415770: Multiply.
%285x%2B7%29%28x%5E3-x%2B7%29



Trying to understand these can you show me how this is done through each step. thank you.
Found 2 solutions by htmentor, ewatrrr:
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply each term of the 2nd expression by the 1st:
%285x%2B7%29x%5E3+-+%285x%2B7%29x+%2B+%285x%2B7%297
Multiplying terms gives 5x%5E4+%2B+7x%5E3+-+5x%5E2+-+7x+%2B+35x+%2B+49
Collecting like terms, we have 5x%5E4+%2B+7x%5E3+-+5x%5E2+%2B+28x+%2B+49
Quick check.
Let x=1:
((5)(1)+7)(1^3-1+7 -> (12)(7) = 84
(5)(1^4)+(7)(1)^3-(5)(1^2)+(28)(1)+49 -> 5+7-5+28+49=84

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Multiply.



%285x%2B7%29%28x%5E3-x%2B7%29         |Expanding so as to combine Like terms 

5x(x^3-x+7) + 7(x^3-x+7) 

5x^4 - 5x^2 + 35x + 7x^3 - 7x + 49     |combining Like terms

  5x^2 + 7x^3- 5x^2 + 28x + 49     |completed!