How to Solve the Complex Polynomial Product Equation?

[anandzoom]

(1+x+x²+x³+x⁴+x⁵+x⁶+x⁷+x⁸)(1+x²+x⁴+x⁶+x⁸)(1+x³+x⁶)(1+x⁴+x⁸)(1+x⁵)(1+x⁶)(1+x⁷)(1+x⁸) = 1+x+2x²+3x³+5x⁴+7x⁵+11x⁶+15x⁷+22x⁸+...+x⁵⁶
Please explain me the step-wise procedure to arrive at the solution.

 

[SammyS]

(1+x+x2+x3+x4+x5+x6+x7+x8)(1+x2+x4+x6+x8)(1+x3+x6)(1+x4+x8)(1+x5)(1+x6)(1+x7)(1+x8) = 1+x+2x2+3x3+5x4+7x5+11x6+15x7+22x8+...+x56
Please explain me the step-wise procedure to arrive at the solution.

Are those supposed to be exponents on the variable, x ?

Use that X² feature in the green bar above the edit/composition box.
This gives something like: (1+x+x²+x³+x⁴+x⁵+x⁶+x⁷+x⁸)(1+x²+x⁴+x⁶+x⁸) ...

Furthermore:
You should use the supplied template when starting a thread, as well as showing an attempt at solving/understanding the problem you're presenting.

 

[FactChecker]

The only way I see to solve it is to multiply out the left side. Then move everything to one side and hope that many of the high-exponent terms disappear. Maybe there will only be a low order polynomial left. Look for the zeros of the polynomial.

 

[HallsofIvy]

Assuming those are exponents, that is a polynomial equation of degree 56. There exist "formulas" for polynomial equations of degree 4 or less but there is NO 'step by step" way of solving a general polynomial of degree five or higher and certainly not 56!

 

[FactChecker]

Assuming those are exponents, that is a polynomial equation of degree 56. There exist "formulas" for polynomial equations of degree 4 or less but there is NO 'step by step" way of solving a general polynomial of degree five or higher and certainly not 56!

I noticed that the x⁵⁶ term cancels out. I assume the question has been rigged so that many terms cancel out.

 

[anandzoom]

I noticed that the x⁵⁶ term cancels out. I assume the question has been rigged so that many terms cancel out.

Everything is in '+' ... terms can cancel out only if there is some '-' if I'm right

 

[FactChecker]

Everything is in '+' ... terms can cancel out only if there is some '-' if I'm right

Notice that both sides have +x⁵⁶. (To see that on the left, scan through all that multiplication and notice that all the highest power terms multiply out to +x⁵⁶⁾. ) You can subtract x⁵⁶ from both sides and the rest stays equal. My guess is that a lot of the high-power terms cancel out just like x⁵⁶.

 

[SammyS]

Notice that both sides have +x⁵⁶. (To see that on the left, scan through all that multiplication and notice that all the highest power terms multiply out to +x⁵⁶⁾. ) You can subtract x⁵⁶ from both sides and the rest stays equal. My guess is that a lot of the high-power terms cancel out just like x⁵⁶.

My guess is that the right hand side is merely the expansion of the left hand side, so they ALL cancel.

OP still has not complied with PF rules.

 

[NascentOxygen]

In the homework help forums, posts seeking assistance must be accompanied by evidence of the member's attempt at solving the problem. No such evidence has been provided here.

Thread closed.