Question 118317
{{{(4ab-1)^2}}} Start with the given expression



{{{(4ab-1)(4ab-1)}}} Expand. Something like {{{x^2}}} is the same as {{{x*x}}}


Now let's foil the expression



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



{{{(highlight(4ab)-1)(highlight(4ab)-1)}}} Multiply the First terms:{{{(4ab)*(4ab)=16a^2b^2}}}



{{{(highlight(4ab)-1)(4ab+highlight(-1))}}} Multiply the Outer terms:{{{(4ab)*(-1)=-4ab}}}



{{{(4ab+highlight(-1))(highlight(4ab)-1)}}} Multiply the Inner terms:{{{(-1)*(4ab)=-4ab}}}



{{{(4ab+highlight(-1))(4ab+highlight(-1))}}} Multiply the Last terms:{{{(-1)*(-1)=1}}}



{{{16a^2b^2-4ab-4ab+1}}} Now collect every term to make a single expression




{{{16a^2b^2-8ab+1}}} Now combine like terms



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Answer:

So {{{(4ab-1)(4ab-1)}}} foils and simplifies to  {{{16a^2b^2-8ab+1}}}


In other words, {{{(4ab-1)(4ab-1)=16a^2b^2-8ab+1}}}



note: there is another way to do this problem, but I'm not sure if your math class has covered it or not.