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

[dlecl]

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

 

[cbarker1]

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.

 

[Greg]

Hey, it's not an equation it's an expression!

Here's what an online CAS thinks.

 

[Opalg]

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.