Question 145203
First FOIL {{{( 4 x + 1 ) ^ 2}}}


{{{(2x-4)^2}}} Start with the given expression



{{{(4x+1)(4x+1)}}} 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(4x)+1)(highlight(4x)+1)}}} Multiply the <font color="red">F</font>irst terms:{{{(4x)*(4x)=16x^2}}}



{{{(highlight(4x)+1)(4x+highlight(1))}}} Multiply the <font color="red">O</font>uter terms:{{{(4x)*(1)=4x}}}



{{{(4x+highlight(1))(highlight(4x)+1)}}} Multiply the <font color="red">I</font>nner terms:{{{(1)*(4x)=4x}}}



{{{(4x+highlight(1))(4x+highlight(1))}}} Multiply the <font color="red">L</font>ast terms:{{{(1)*(1)=1}}}



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




{{{16x^2+8x+1}}} Now combine like terms



So {{{(4x+1)^2}}} foils and simplifies to  {{{16x^2+8x+1}}}


In other words, {{{(4x+1)^2=16x^2+8x+1}}}





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Now let's FOIL {{{(2 x - 4 )^ 2 }}}




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



{{{(highlight(2x)-4)(2x+highlight(-4))}}} Multiply the <font color="red">O</font>uter terms:{{{(2x)*(-4)=-8x}}}



{{{(2x+highlight(-4))(highlight(2x)-4)}}} Multiply the <font color="red">I</font>nner terms:{{{(-4)*(2x)=-8x}}}



{{{(2x+highlight(-4))(2x+highlight(-4))}}} Multiply the <font color="red">L</font>ast terms:{{{(-4)*(-4)=16}}}



{{{4x^2-8x-8x+16}}} Now collect every term to make a single expression




{{{4x^2-16x+16}}} Now combine like terms



So {{{(2x-4)^2}}} foils and simplifies to  {{{4x^2-16x+16}}}


In other words, {{{(2x-4)^2=4x^2-16x+16}}}





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So {{{( 4 x + 1 ) ^ 2+ (2 x - 4 )^ 2 }}} now becomes {{{(16x^2+8x+1)+(4x^2-16x+16)}}}



{{{(16x^2+8x+1)+(4x^2-16x+16)}}} Start with the given expression



{{{20x^2-8x+17}}} Combine like terms




So {{{( 4 x + 1 ) ^ 2+ (2 x - 4 )^ 2=20x^2-8x+17}}}