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(34x^15+19x^98)(54x^54+76x^34)

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Hello!

It isn't clear what the problem is. I see two variants: extract some more factors (factor completely) and, to the contrast, open the parentheses (express as a sum of monomials). Let's do both tasks.

1. Factoring.

34 and 19 have no common factors (34=2*17), `x^15` and `x^98` have the greatest common factor (GCF) `x^15.` Also, 54 and 76 have GCF 2 (54=`2*3^3,` 76=`2^2*19`). And GCF of `x^54` and `x^34` is `x^34` (the less power).

And the most factored form is:

`x^15(34+19x^83)*2x^34(27x^20+38)=2x^49(34+19x^83)(27x^20+38).`

 

2. Making a sum.

To multiply two binomials we have to multiply each term by each and sum the results: (a+b)(u+v)=au+av+bu+bv.

 

So `(34x^15+19x^98)(54x^54+76x^34)=`

`=34*54x^(15+54)+34*76x^(15+34)+19*54x^(98+54)*19*76x^(98+34)=`

`=1836x^69+2584x^49+1026x^152+1444x^132.`

 

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