Simplify a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd)

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Discussion Overview

The discussion revolves around the simplification of the expression involving four variables a, b, c, and d: a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd). Participants explore whether this expression can be reduced to a simpler form.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant suggests that the expression cannot be simplified due to the absence of a common factor in the polynomial.
  • Another participant corrects a previous statement by noting that the expression is not an equation but rather an expression.
  • A later reply presents a potential simplification, proposing that the expression can be rewritten as $\frac12(2a+1)(2b+1)(2c+1)(2d+1) - \frac12$.

Areas of Agreement / Disagreement

Participants express differing views on the simplification of the expression, with no consensus reached on whether it can be simplified further beyond the proposed form.

Contextual Notes

Some participants may have differing interpretations of the expression's nature, and the proposed simplification may depend on specific algebraic manipulations that are not universally agreed upon.

dlecl
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four variables a,b,c,d
here is the equation: a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd)
wondering if this can be simplified to something much smaller
 
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dlecl said:
four variables a,b,c,d
here is the equation: a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd)
wondering if this can be simplified to something much smaller

The answer to your question is not really because there is not a common factor in the polynomial.
 
Hey, it's not an equation it's an expression!

Here's what an online CAS thinks.
 
dlecl said:
four variables a,b,c,d
here is the equation: a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd)
wondering if this can be simplified to something much smaller
You could write it as $\frac12(2a+1)(2b+1)(2c+1)(2d+1) - \frac12$, if that helps.
 

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