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1) n²-6n+9-(n²-4)=n²-6n+9-n²+4=-6n+13
7) ((x+y)+1)((x+y)-1)=(x+y)²-1=x²+2xy+y²+1
8)![frac{ 4^{n}(4 ^{2}-1)* 5^{n} }{ 5^{n}* 3^{n}*15* 3^{-n}* 4^{-n}}= frac{ 4^{n}(16-1) }{3^{n}*15* 3^{-n}* 4^{-n}}= frac{ 4^{n}*15*4^{n} * 3^{n} }{3^{n}*15}= 4^{n+n}= 4^{2n} frac{ 4^{n}(4 ^{2}-1)* 5^{n} }{ 5^{n}* 3^{n}*15* 3^{-n}* 4^{-n}}= frac{ 4^{n}(16-1) }{3^{n}*15* 3^{-n}* 4^{-n}}= frac{ 4^{n}*15*4^{n} * 3^{n} }{3^{n}*15}= 4^{n+n}= 4^{2n}](https://tex.z-dn.net/?f=+frac%7B+4%5E%7Bn%7D%284+%5E%7B2%7D-1%29%2A+5%5E%7Bn%7D+%7D%7B+5%5E%7Bn%7D%2A+3%5E%7Bn%7D%2A15%2A+3%5E%7B-n%7D%2A+4%5E%7B-n%7D%7D%3D++frac%7B+4%5E%7Bn%7D%2816-1%29+%7D%7B3%5E%7Bn%7D%2A15%2A+3%5E%7B-n%7D%2A+4%5E%7B-n%7D%7D%3D+frac%7B+4%5E%7Bn%7D%2A15%2A4%5E%7Bn%7D+%2A+3%5E%7Bn%7D++%7D%7B3%5E%7Bn%7D%2A15%7D%3D+4%5E%7Bn%2Bn%7D%3D+4%5E%7B2n%7D)
9)![frac{4y}{x(x-3y)}- frac{x}{y(x-3y)} * frac{xy(3y-x)}{ x^{2} -4 y^{2} } = frac{4 y^{2}- x^{2} }{xy(x-3y)}*frac{xy(3y-x)}{ x^{2} -4 y^{2} }= frac{4y}{x(x-3y)}- frac{x}{y(x-3y)} * frac{xy(3y-x)}{ x^{2} -4 y^{2} } = frac{4 y^{2}- x^{2} }{xy(x-3y)}*frac{xy(3y-x)}{ x^{2} -4 y^{2} }=](https://tex.z-dn.net/?f=+frac%7B4y%7D%7Bx%28x-3y%29%7D-+frac%7Bx%7D%7By%28x-3y%29%7D+%2A+frac%7Bxy%283y-x%29%7D%7B+x%5E%7B2%7D+-4+y%5E%7B2%7D+%7D++%3D+frac%7B4+y%5E%7B2%7D-+x%5E%7B2%7D++%7D%7Bxy%28x-3y%29%7D%2Afrac%7Bxy%283y-x%29%7D%7B+x%5E%7B2%7D+-4+y%5E%7B2%7D+%7D%3D)
7) ((x+y)+1)((x+y)-1)=(x+y)²-1=x²+2xy+y²+1
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