Question 198011
If "A" and "B" are two binomials which add to a third binomial "C", then this means that {{{A+B=C}}}. If we know what "A" and "C" are, then we can subtract "A" from both sides to solve for "B" like so:


{{{B=C-A}}}




So in this case, {{{C=3x^2-5x}}}, {{{A=2x^2-x}}}, and "B" is our unknown binomial


{{{B=C-A}}} Start with the given equation.



{{{B=(3x^2-5x)-(2x^2-x)}}} Plug in {{{C=3x^2-5x}}} and {{{A=2x^2-x}}}



{{{B=3x^2-5x-2x^2+x}}} Distribute



{{{B=x^2-4x}}} Combine like terms.



So the unknown binomial is {{{x^2-4x}}}