Question 597290


{{{(q+5)(5q-1)}}} Start with the given expression.



Now let's FOIL the expression.



Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(q)+5)(highlight(5q)-1)}}} Multiply the <font color="red">F</font>irst terms:{{{(q)*(5*q)=5*q^2}}}.



{{{(highlight(q)+5)(5q+highlight(-1))}}} Multiply the <font color="red">O</font>uter terms:{{{(q)*(-1)=-q}}}.



{{{(q+highlight(5))(highlight(5q)-1)}}} Multiply the <font color="red">I</font>nner terms:{{{(5)*(5*q)=25*q}}}.



{{{(q+highlight(5))(5q+highlight(-1))}}} Multiply the <font color="red">L</font>ast terms:{{{(5)*(-1)=-5}}}.



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So we have the terms: {{{5*q^2}}}, {{{-q}}}, {{{25*q}}}, {{{-5}}} 



{{{5*q^2-q+25*q-5}}} Now add every term listed above to make a single expression.



{{{5q^2+24q-5}}} Now combine like terms.



So {{{(q+5)(5q-1)}}} FOILs to {{{5q^2+24q-5}}}.



In other words, {{{(q+5)(5q-1)=5q^2+24q-5}}} for all values of 'q'.