Is it possible to isolate $ac/bc/bd$ from the equation $x=ab+cd$?
By Sarah Rodriguez •
Here is a tricky algebra problem I couldn't figure out, I am wondering if anyone else could, or if it's even possible. $$ x = ab + cd$$ The goal is to completely isolate ac (or $bc$ or $bd$ or $ad$ it doesn't matter)
Everything I try results in $a$ or $c$ being stuck somewhere on both sides.
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$\begingroup$It can't be done.
More precisely, from the equation$$ x=ab+cd $$it's not possible to solve for $ac$ in terms of $b,d,x$.
For example, suppose $b=d=x=1$.
Then the equation reduces to$$ a+c=1 $$so for any choice of $a$ we get$$ ac=a(1-a) $$which varies with $a$.
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