Question 185543


{{{(5x^2-1)^2}}} Start with the given expression.



{{{(5x^2-1)(5x^2-1)}}} Expand. Remember something like {{{A^2=A*A}}}.



Now let's FOIL the expression.



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



{{{(highlight(5x^2)-1)(highlight(5x^2)-1)}}} Multiply the <font color="red">F</font>irst terms:{{{(5*x^2)*(5*x^2)=25*x^4}}}.



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



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



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



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So we have the terms: {{{25*x^4}}}, {{{-5*x^2}}}, {{{-5*x^2}}}, and {{{1}}} 



{{{25*x^4-5*x^2-5*x^2+1}}} Now add every term listed above to make a single expression.



{{{25*x^4-10*x^2+1}}} Now combine like terms.



So {{{(5x^2-1)^2}}} FOILs to {{{25*x^4-10*x^2+1}}}.



In other words, {{{(5x^2-1)^2=25*x^4-10*x^2+1}}}.