Question 197662


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



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



Now let's FOIL the expression.



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



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



{{{(highlight(5x)-2)(5x+highlight(-2))}}} Multiply the <font color="red">O</font>uter terms:{{{(5*x)*(-2)=-10*x}}}.



{{{(5x+highlight(-2))(highlight(5x)-2)}}} Multiply the <font color="red">I</font>nner terms:{{{(-2)*(5*x)=-10*x}}}.



{{{(5x+highlight(-2))(5x+highlight(-2))}}} Multiply the <font color="red">L</font>ast terms:{{{(-2)*(-2)=4}}}.



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So we have the terms: {{{25*x^2}}}, {{{-10*x}}}, {{{-10*x}}}, {{{4}}} 



{{{25*x^2-10*x-10*x+4}}} Now add every term listed above to make a single expression.



{{{25*x^2-20*x+4}}} Now combine like terms.



So {{{(5x-2)^2}}} FOILs to {{{25*x^2-20*x+4}}}.



In other words, {{{(5x-2)^2=25*x^2-20*x+4}}}.