Ответ:
Объяснение:
Решение
3.
а) =
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Answers & Comments
Ответ:
Объяснение:
Решение
3.
а) =![(z-w)*(z^{2} +zw+w^{2} )=(z-w)*(z^{2}+wz+w^{2} ) (z-w)*(z^{2} +zw+w^{2} )=(z-w)*(z^{2}+wz+w^{2} )](https://tex.z-dn.net/?f=%28z-w%29%2A%28z%5E%7B2%7D%20%2Bzw%2Bw%5E%7B2%7D%20%29%3D%28z-w%29%2A%28z%5E%7B2%7D%2Bwz%2Bw%5E%7B2%7D%20%29)
б)![=u^{3}+3^{3} =(u+3)*(u^{2} -u*3+3^{2} )=(u+3)*(u^{2} -3u+9) =u^{3}+3^{3} =(u+3)*(u^{2} -u*3+3^{2} )=(u+3)*(u^{2} -3u+9)](https://tex.z-dn.net/?f=%3Du%5E%7B3%7D%2B3%5E%7B3%7D%20%20%3D%28u%2B3%29%2A%28u%5E%7B2%7D%20-u%2A3%2B3%5E%7B2%7D%20%29%3D%28u%2B3%29%2A%28u%5E%7B2%7D%20-3u%2B9%29)
в)![=\frac{1}{8} *(8x^{3}-1)=\frac{1}{8}*(2x-1)*(4x^{2} +2x+1) =\frac{1}{8} *(8x^{3}-1)=\frac{1}{8}*(2x-1)*(4x^{2} +2x+1)](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B8%7D%20%2A%288x%5E%7B3%7D-1%29%3D%5Cfrac%7B1%7D%7B8%7D%2A%282x-1%29%2A%284x%5E%7B2%7D%20%2B2x%2B1%29)
г)![=\frac{1}{125}-t^{3} = \frac{1}{125}*(1-125t^{3})=\frac{1}{125}*(1-5t)*(1+5t+25t^{2} ) =\frac{1}{125}-t^{3} = \frac{1}{125}*(1-125t^{3})=\frac{1}{125}*(1-5t)*(1+5t+25t^{2} )](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B125%7D-t%5E%7B3%7D%20%3D%20%5Cfrac%7B1%7D%7B125%7D%2A%281-125t%5E%7B3%7D%29%3D%5Cfrac%7B1%7D%7B125%7D%2A%281-5t%29%2A%281%2B5t%2B25t%5E%7B2%7D%20%29)
д)![=\frac{1}{1000}+z^{3}=\frac{1}{1000}*(1+1000z^{3}) = \frac{1}{1000}*(1+10z)*(1-10z+100z^{2}) =\frac{1}{1000}+z^{3}=\frac{1}{1000}*(1+1000z^{3}) = \frac{1}{1000}*(1+10z)*(1-10z+100z^{2})](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B1000%7D%2Bz%5E%7B3%7D%3D%5Cfrac%7B1%7D%7B1000%7D%2A%281%2B1000z%5E%7B3%7D%29%20%3D%20%5Cfrac%7B1%7D%7B1000%7D%2A%281%2B10z%29%2A%281-10z%2B100z%5E%7B2%7D%29)
е)![=\frac{1}{27}*(1+27c^{3})=\frac{1}{27}*(1+3c)*(1-3c+9c^{2} ) =\frac{1}{27}*(1+27c^{3})=\frac{1}{27}*(1+3c)*(1-3c+9c^{2} )](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B27%7D%2A%281%2B27c%5E%7B3%7D%29%3D%5Cfrac%7B1%7D%7B27%7D%2A%281%2B3c%29%2A%281-3c%2B9c%5E%7B2%7D%20%29)
ж)![=(a^{2}+c)*(a^{4}-a^{2}c+c^{2} ) =(a^{2}+c)*(a^{4}-a^{2}c+c^{2} )](https://tex.z-dn.net/?f=%3D%28a%5E%7B2%7D%2Bc%29%2A%28a%5E%7B4%7D-a%5E%7B2%7Dc%2Bc%5E%7B2%7D%20%29)
з)![=x^{3*3}-y^{3*4} =(x^{3})^{3} -(y^{4})^{3} =(x^{3}-y^{4} )*((x^{3})^{2} +x^{3}y^{4}+(y^{4})^{2})=(x^{3}-y^{4} )*(x^{6}+x^{3}y^{4}+y^{8}) =x^{3*3}-y^{3*4} =(x^{3})^{3} -(y^{4})^{3} =(x^{3}-y^{4} )*((x^{3})^{2} +x^{3}y^{4}+(y^{4})^{2})=(x^{3}-y^{4} )*(x^{6}+x^{3}y^{4}+y^{8})](https://tex.z-dn.net/?f=%3Dx%5E%7B3%2A3%7D-y%5E%7B3%2A4%7D%20%3D%28x%5E%7B3%7D%29%5E%7B3%7D%20-%28y%5E%7B4%7D%29%5E%7B3%7D%20%3D%28x%5E%7B3%7D-y%5E%7B4%7D%20%29%2A%28%28x%5E%7B3%7D%29%5E%7B2%7D%20%2Bx%5E%7B3%7Dy%5E%7B4%7D%2B%28y%5E%7B4%7D%29%5E%7B2%7D%29%3D%28x%5E%7B3%7D-y%5E%7B4%7D%20%29%2A%28x%5E%7B6%7D%2Bx%5E%7B3%7Dy%5E%7B4%7D%2By%5E%7B8%7D%29)
и)![=3^{3}a^{3}-c^{3}=(3a)^{3}-c^{3}=( 3a-c)*((3a)^{2} +3ac+c^{2} )=(3a-c)*(9a^{2} +3ac+c^{2}) =3^{3}a^{3}-c^{3}=(3a)^{3}-c^{3}=( 3a-c)*((3a)^{2} +3ac+c^{2} )=(3a-c)*(9a^{2} +3ac+c^{2})](https://tex.z-dn.net/?f=%3D3%5E%7B3%7Da%5E%7B3%7D-c%5E%7B3%7D%3D%283a%29%5E%7B3%7D-c%5E%7B3%7D%3D%28%203a-c%29%2A%28%283a%29%5E%7B2%7D%20%2B3ac%2Bc%5E%7B2%7D%20%29%3D%283a-c%29%2A%289a%5E%7B2%7D%20%2B3ac%2Bc%5E%7B2%7D%29)
к)
л)
м)![=1000v^{9} -\frac{1}{1000}w^{6} =(10v^{3}-\frac{1}{10}w^{2})*(100v^{6} +v^{3}w^{2}+0.01w^{4} ) =1000v^{9} -\frac{1}{1000}w^{6} =(10v^{3}-\frac{1}{10}w^{2})*(100v^{6} +v^{3}w^{2}+0.01w^{4} )](https://tex.z-dn.net/?f=%3D1000v%5E%7B9%7D%20-%5Cfrac%7B1%7D%7B1000%7Dw%5E%7B6%7D%20%3D%2810v%5E%7B3%7D-%5Cfrac%7B1%7D%7B10%7Dw%5E%7B2%7D%29%2A%28100v%5E%7B6%7D%20%2Bv%5E%7B3%7Dw%5E%7B2%7D%2B0.01w%5E%7B4%7D%20%29)