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You can put this solution on YOUR website!
This is a good question! It is both the difference of two perfect squares and the difference of two perfect cubes. I am choosing to attack the squares first and then the cubes. There are three formulas that I am going to use.
\n" ); document.write( "u^2-v^2=(u+v)(u-v)
\n" ); document.write( "u^3-v^3=(u-v)(u^2+uv+v^2)
\n" ); document.write( "u^3+v^3=(u+v)(u^2-uv+v^2)
\n" ); document.write( "When I simplify, I'm going to need to foil or remember:
\n" ); document.write( "(u+v)^2=u^2+2uv+v^2
\n" ); document.write( "(u-v)^2=u^2-2uv+v^2
\n" ); document.write( "(u+v)(u-v)=u^2-v^2
\n" ); document.write( "So lets get started:
\n" ); document.write( "(a+b)^6-(a-b)^6
\n" ); document.write( "=((a+b)^3)^2-((a-b)^3)^2
\n" ); document.write( "=((a+b)^3+(a-b)^3)((a+b)^3-(a-b)^3)
\n" ); document.write( "=((a+b)+(a-b))((a+b)^2-(a+b)(a-b)+(a-b)^2)((a+b)-(a-b))((a+b)^2+(a+b)(a-b)+(a-b)^2)
\n" ); document.write( "Now simplify and combine like terms:
\n" ); document.write( "=((a+b)+(a-b))((a^2+2ab+b^2)-(a^2-b^2)+(a^2-2ab+b^2))((a+b)-(a-b))((a^2+2ab+b^2)+(a^2-b^2)+(a^2-2ab+b^2))
\n" ); document.write( "=(a+b+a-b)(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2)(a+b-a+b)(a^2+2ab+b^2+a^2-b^2+a^2+2ab+b^2)
\n" ); document.write( "=(2a)(a^2+3b^2)(2b)(3a^2+b^2)
\n" ); document.write( "=(2a)(2b)(a^2+3b^2)(3a^2+b^2)
\n" ); document.write( "=4ab(a^2+3b^2)(3a^2+b^2) \n" ); document.write( "