Question 103798
First think of two numbers that multiply to -12 (the last coefficient) and add to 4 (the second coefficient)



So after going through a list of numbers we get the numbers 6 and -2. These numbers both multiply to -12 and add to 4 (ie -6+2=4 and -6*2=-12)



So now rewrite the expression {{{m^2 + 4mn - 12n^2}}} by replacing the 4mn with 6mn-2mn (remember they add to 4)


{{{m^2 + 6mn -2mn- 12n^2}}}



{{{(m^2 + 6mn)+( -2mn- 12n^2)}}} Group like terms



{{{m(m + 6n)-2n( m+ 6n)}}} Factor out the GCF out of each group



{{{(m-2n)(m + 6n)}}} Combine like terms



So {{{m^2 + 4mn - 12n^2}}} factors to {{{(m-2n)(m + 6n)}}}. Notice how {{{(m-2n)(m + 6n)}}} foils to {{{m^2 + 4mn - 12n^2}}}