Question 177430


{{{(5a-3b)^2}}} Start with the given expression.



{{{(5a-3b)(5a-3b)}}} 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(5a)-3b)(highlight(5a)-3b)}}} Multiply the <font color="red">F</font>irst terms:{{{(5*a)*(5*a)=25*a^2}}}.



{{{(highlight(5a)-3b)(5a+highlight(-3b))}}} Multiply the <font color="red">O</font>uter terms:{{{(5*a)*(-3*b)=-15*a*b}}}.



{{{(5a+highlight(-3b))(highlight(5a)-3b)}}} Multiply the <font color="red">I</font>nner terms:{{{(-3*b)*(5*a)=-15*a*b}}}.



{{{(5a+highlight(-3b))(5a+highlight(-3b))}}} Multiply the <font color="red">L</font>ast terms:{{{(-3*b)*(-3*b)=9*b^2}}}.



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{{{25*a^2-15*a*b-15*a*b+9*b^2}}} Now collect every term to make a single expression.



{{{25*a^2-30*a*b+9*b^2}}} Now combine like terms.



So {{{(5a-3b)^2}}} FOILs to {{{25*a^2-30*a*b+9*b^2}}}.



In other words, {{{(5a-3b)^2=25*a^2-30*a*b+9*b^2}}}.