Ответ:
#1
е) (a−b)(a+b)(a2+b2)(a4+b4)= (a2+ab−ba−b2)(a2+b2)(a4+b4)=(a2+ab−ba−b2)(a2+b2)(a4+b4)=(a2−b2)(a2+b2)(a4+b4)= (a4+a2b2−b2a2−b4)(a4+b4)(a4+a2b2−b2a2−b4)(a4+b4)=(a4−b4)(a4+b4)=a8+a4b4−b4a4−b8=a8+a4b4−b4a4−b8=a8−b8=a8−b8
#2
а)201*199=200*(200-1)+199=200*200-200+199=200*200-1=40000-1=39999
б)74*66=7884
в)29.8*30,2=899,96
#3
формула квадратов (a+b)^2=a^2+2ab+b^2
а)(y+4)^2=y*y+4*y+4*y+4*4=
в)
б)
г)
д)
е)
#4
а)
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Answers & Comments
Ответ:
#1
е) (a−b)(a+b)(a2+b2)(a4+b4)= (a2+ab−ba−b2)(a2+b2)(a4+b4)=(a2+ab−ba−b2)(a2+b2)(a4+b4)=(a2−b2)(a2+b2)(a4+b4)= (a4+a2b2−b2a2−b4)(a4+b4)(a4+a2b2−b2a2−b4)(a4+b4)=(a4−b4)(a4+b4)=a8+a4b4−b4a4−b8=a8+a4b4−b4a4−b8=a8−b8=a8−b8
#2
а)201*199=200*(200-1)+199=200*200-200+199=200*200-1=40000-1=39999
б)74*66=7884
в)29.8*30,2=899,96
#3
формула квадратов (a+b)^2=a^2+2ab+b^2
а)(y+4)^2=y*y+4*y+4*y+4*4=
в)
б)![9-6a+a^{2} 9-6a+a^{2}](https://tex.z-dn.net/?f=9-6a%2Ba%5E%7B2%7D)
г)![(-m-3n)^{2}=-(m+3n)^{2} \\ > при взятии скобки в квадрат знак минус сократиться</p><p><img src=](https://tex.z-dn.net/?f=%28-m-3n%29%5E%7B2%7D%3D-%28m%2B3n%29%5E%7B2%7D%20%5C%5C)
д)![\frac{4}{25}x^{4}+\frac{4}{10} x^{2}y+\frac{1}{4}y^{2}=\frac{4}{25}x^{4}+\frac{2}{5} x^{2}y+\frac{1}{4}y^{2} \frac{4}{25}x^{4}+\frac{4}{10} x^{2}y+\frac{1}{4}y^{2}=\frac{4}{25}x^{4}+\frac{2}{5} x^{2}y+\frac{1}{4}y^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B25%7Dx%5E%7B4%7D%2B%5Cfrac%7B4%7D%7B10%7D%20x%5E%7B2%7Dy%2B%5Cfrac%7B1%7D%7B4%7Dy%5E%7B2%7D%3D%5Cfrac%7B4%7D%7B25%7Dx%5E%7B4%7D%2B%5Cfrac%7B2%7D%7B5%7D%20x%5E%7B2%7Dy%2B%5Cfrac%7B1%7D%7B4%7Dy%5E%7B2%7D)
е)![m^{4} b^{8} - 2a^{5} m^{2} b^{4}n+n^{2} a^{10} m^{4} b^{8} - 2a^{5} m^{2} b^{4}n+n^{2} a^{10}](https://tex.z-dn.net/?f=m%5E%7B4%7D%20b%5E%7B8%7D%20-%202a%5E%7B5%7D%20m%5E%7B2%7D%20b%5E%7B4%7Dn%2Bn%5E%7B2%7D%20a%5E%7B10%7D)
#4
а)![(5x+7y)^2-70xy=25x^{2}+70xy+49y^{2} -70xy=25x^{2} +49y^{2} (5x+7y)^2-70xy=25x^{2}+70xy+49y^{2} -70xy=25x^{2} +49y^{2}](https://tex.z-dn.net/?f=%285x%2B7y%29%5E2-70xy%3D25x%5E%7B2%7D%2B70xy%2B49y%5E%7B2%7D%20-70xy%3D25x%5E%7B2%7D%20%2B49y%5E%7B2%7D)
б)![4m-m^{2}+16-8m+m^{2} =16-4m=4(4-m) 4m-m^{2}+16-8m+m^{2} =16-4m=4(4-m)](https://tex.z-dn.net/?f=4m-m%5E%7B2%7D%2B16-8m%2Bm%5E%7B2%7D%20%3D16-4m%3D4%284-m%29)
в)![x^{2} -16x+64-2(36-12x+x^{2} )=x^{2} -16x+64-72+24x-2x^{2} =8x-8-x^{2} x^{2} -16x+64-2(36-12x+x^{2} )=x^{2} -16x+64-72+24x-2x^{2} =8x-8-x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-16x%2B64-2%2836-12x%2Bx%5E%7B2%7D%20%29%3Dx%5E%7B2%7D%20-16x%2B64-72%2B24x-2x%5E%7B2%7D%20%3D8x-8-x%5E%7B2%7D)
г)![4a^{2} -12ab+9b^{2} +9a^{2}+12ab+4b^{2}=13a^{2} +13b^{2} =13(a^{2}+b^{2}) 4a^{2} -12ab+9b^{2} +9a^{2}+12ab+4b^{2}=13a^{2} +13b^{2} =13(a^{2}+b^{2})](https://tex.z-dn.net/?f=4a%5E%7B2%7D%20-12ab%2B9b%5E%7B2%7D%20%2B9a%5E%7B2%7D%2B12ab%2B4b%5E%7B2%7D%3D13a%5E%7B2%7D%20%2B13b%5E%7B2%7D%20%3D13%28a%5E%7B2%7D%2Bb%5E%7B2%7D%29)
д)![25p^{2} +30pd+9d^{2} -(25p^{2} -30pd+9d^{2} )-60pd=25p^{2} +30pd+9d^{2}-25p^{2}+30pd-9d^{2}-60pd=0 25p^{2} +30pd+9d^{2} -(25p^{2} -30pd+9d^{2} )-60pd=25p^{2} +30pd+9d^{2}-25p^{2}+30pd-9d^{2}-60pd=0](https://tex.z-dn.net/?f=25p%5E%7B2%7D%20%2B30pd%2B9d%5E%7B2%7D%20-%2825p%5E%7B2%7D%20-30pd%2B9d%5E%7B2%7D%20%29-60pd%3D25p%5E%7B2%7D%20%2B30pd%2B9d%5E%7B2%7D-25p%5E%7B2%7D%2B30pd-9d%5E%7B2%7D-60pd%3D0)