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

dlecl

New member
Sep 18, 2019
1
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

Active member
Jan 8, 2013
236
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

Perseverance
Staff member
Feb 5, 2013
1,382
Hey, it's not an equation it's an expression!

Here's what an online CAS thinks.
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,679
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.