The expression a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd) cannot be simplified significantly due to the absence of common factors among the terms. It is clarified that this is an expression, not an equation. A potential reformulation of the expression is given as $\frac12(2a+1)(2b+1)(2c+1)(2d+1) - \frac12$, which provides a more compact representation.
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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
You could write it as $\frac12(2a+1)(2b+1)(2c+1)(2d+1) - \frac12$, if that helps.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