Question 367280


{{{(v^2+v-1)(v^2+5v-7)}}} Start with the given expression.



{{{v^2(v^2+5v-7)+v(v^2+5v-7)-1(v^2+5v-7)}}} Expand. Remember that {{{(A+B+C)(D+E+F)=A(D+E+F)+B(D+E+F)+C(D+E+F)}}}



{{{(v^2)*(v^2)+(v^2)*(5v)+(v^2)*(-7)+(v)*(v^2)+(v)*(5v)+(v)*(-7)+(-1)*(v^2)+(-1)*(5v)+(-1)*(-7)}}} Distribute.



{{{v^4+5*v^3-7*v^2+v^3+5*v^2-7*v-v^2-5*v+7}}} Multiply.



{{{v^4+6*v^3-3*v^2-12*v+7}}} Now combine like terms.



 So {{{(v^2+v-1)(v^2+5v-7)}}} expands to {{{v^4+6*v^3-3*v^2-12*v+7}}}.



In other words, {{{(v^2+v-1)(v^2+5v-7)=v^4+6*v^3-3*v^2-12*v+7}}}.



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