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2 апреля 2023 21:51
954
Представьте в виде многочлена 1)33.1
2) 33.2
3)33.3
![image](https://539619.selcdn.ru/cdn-znarium-com/qa/83-8eed419fc77a9d-7a9d9c3.jpg)
1
ответ
Все примеры решаем по двум формулам.
Куб суммы: (a + b)³ = a³ + 3a²b + 3ab² + b³
Куб разности: (a - b)³ = a³ - 3a²b + 3ab² - b³
![\displayctyle\tt 33.1\\1) \ (2+x)^3=2^3+3\cdot2^2\cdot x+3\cdot2\cdot x^2+x^3=x^3+6x^2+12x+8\\2) \ (a-2)^3=a^3-3\cdot a^2\cdot 2+3\cdot a\cdot 2^2-2^3=a^3-6a^2+12a-8\\3)\ (5-b)^3=125-75b+15b^2-b^3=-b^3+15b^2-75b+125\\ 4)\ (y+3)^3=y^3+9y^2+27y+27 \\5) \ (a-c)^3=a^3-3a^2c+3ac^2-c^3\\6) \ (c+d)^3=c^3+3c^2d+3cd^2+d^3\\7) \ (z-t)^3=z^3-3z^2t+3zt^2-t^3\\ 8) \ (k+m)^3=k^3+3k^2m+3km^2+m^3 \displayctyle\tt 33.1\\1) \ (2+x)^3=2^3+3\cdot2^2\cdot x+3\cdot2\cdot x^2+x^3=x^3+6x^2+12x+8\\2) \ (a-2)^3=a^3-3\cdot a^2\cdot 2+3\cdot a\cdot 2^2-2^3=a^3-6a^2+12a-8\\3)\ (5-b)^3=125-75b+15b^2-b^3=-b^3+15b^2-75b+125\\ 4)\ (y+3)^3=y^3+9y^2+27y+27 \\5) \ (a-c)^3=a^3-3a^2c+3ac^2-c^3\\6) \ (c+d)^3=c^3+3c^2d+3cd^2+d^3\\7) \ (z-t)^3=z^3-3z^2t+3zt^2-t^3\\ 8) \ (k+m)^3=k^3+3k^2m+3km^2+m^3](https://tex.z-dn.net/?f=%5Cdisplayctyle%5Ctt%2033.1%5C%5C1%29%20%5C%20%282%2Bx%29%5E3%3D2%5E3%2B3%5Ccdot2%5E2%5Ccdot%20x%2B3%5Ccdot2%5Ccdot%20x%5E2%2Bx%5E3%3Dx%5E3%2B6x%5E2%2B12x%2B8%5C%5C2%29%20%5C%20%28a-2%29%5E3%3Da%5E3-3%5Ccdot%20a%5E2%5Ccdot%202%2B3%5Ccdot%20a%5Ccdot%202%5E2-2%5E3%3Da%5E3-6a%5E2%2B12a-8%5C%5C3%29%5C%20%285-b%29%5E3%3D125-75b%2B15b%5E2-b%5E3%3D-b%5E3%2B15b%5E2-75b%2B125%5C%5C%204%29%5C%20%28y%2B3%29%5E3%3Dy%5E3%2B9y%5E2%2B27y%2B27%20%5C%5C5%29%20%5C%20%28a-c%29%5E3%3Da%5E3-3a%5E2c%2B3ac%5E2-c%5E3%5C%5C6%29%20%5C%20%28c%2Bd%29%5E3%3Dc%5E3%2B3c%5E2d%2B3cd%5E2%2Bd%5E3%5C%5C7%29%20%5C%20%28z-t%29%5E3%3Dz%5E3-3z%5E2t%2B3zt%5E2-t%5E3%5C%5C%208%29%20%5C%20%28k%2Bm%29%5E3%3Dk%5E3%2B3k%5E2m%2B3km%5E2%2Bm%5E3)
![\displayctyle\tt 33.2\\1) \ (4x+1)^3=64x^3+48x^2+12x+1\\ 2) \ (1-3y)^3=1-9y+27y^2-27y^3=-27y^3+27y^2-9y+1\\ 3)\ (5z-2)^3=125z^3-150z^2+60z-8\\4) \ (4x-3)^3=64x^3-144x^2+108z-27\\5) \ (a+2x)^3=a^3+6a^2x+12ax^2+8x^3\\6) \ (2y-3)^3=8y^3-36y^2+54y-27\\7) \ (p-3q)^3=p^3-9p^2q+27pq^2-27q^3\\8) \ (3n-2m)^3=27n^3-54mn^2+36m^2n-8m^3 \displayctyle\tt 33.2\\1) \ (4x+1)^3=64x^3+48x^2+12x+1\\ 2) \ (1-3y)^3=1-9y+27y^2-27y^3=-27y^3+27y^2-9y+1\\ 3)\ (5z-2)^3=125z^3-150z^2+60z-8\\4) \ (4x-3)^3=64x^3-144x^2+108z-27\\5) \ (a+2x)^3=a^3+6a^2x+12ax^2+8x^3\\6) \ (2y-3)^3=8y^3-36y^2+54y-27\\7) \ (p-3q)^3=p^3-9p^2q+27pq^2-27q^3\\8) \ (3n-2m)^3=27n^3-54mn^2+36m^2n-8m^3](https://tex.z-dn.net/?f=%5Cdisplayctyle%5Ctt%2033.2%5C%5C1%29%20%5C%20%284x%2B1%29%5E3%3D64x%5E3%2B48x%5E2%2B12x%2B1%5C%5C%202%29%20%5C%20%281-3y%29%5E3%3D1-9y%2B27y%5E2-27y%5E3%3D-27y%5E3%2B27y%5E2-9y%2B1%5C%5C%203%29%5C%20%285z-2%29%5E3%3D125z%5E3-150z%5E2%2B60z-8%5C%5C4%29%20%5C%20%284x-3%29%5E3%3D64x%5E3-144x%5E2%2B108z-27%5C%5C5%29%20%5C%20%28a%2B2x%29%5E3%3Da%5E3%2B6a%5E2x%2B12ax%5E2%2B8x%5E3%5C%5C6%29%20%5C%20%282y-3%29%5E3%3D8y%5E3-36y%5E2%2B54y-27%5C%5C7%29%20%5C%20%28p-3q%29%5E3%3Dp%5E3-9p%5E2q%2B27pq%5E2-27q%5E3%5C%5C8%29%20%5C%20%283n-2m%29%5E3%3D27n%5E3-54mn%5E2%2B36m%5E2n-8m%5E3)
![\displayctyle\tt 33.3\\1) \ (0.2a+5)^3=0.008a^3+0.6a^2+15a+125\\2) \ (4-0.5b)^3=64-24b+3b^2-0.125b^3\\3) \ (0.6c-5)^3= 0.216c^3-5.4c^2+45c-125\\ 4) \ (\fracd-2)^3=\fracd^3-\fracd^2+6d-8\\5) \bigg \ (\fract+3)^3=\fract^3+t^2+9t+27\\6) \bigg \ (2-\frack)^3=8-3k+\frack^2-\frack^3 \displayctyle\tt 33.3\\1) \ (0.2a+5)^3=0.008a^3+0.6a^2+15a+125\\2) \ (4-0.5b)^3=64-24b+3b^2-0.125b^3\\3) \ (0.6c-5)^3= 0.216c^3-5.4c^2+45c-125\\ 4) \ (\fracd-2)^3=\fracd^3-\fracd^2+6d-8\\5) \bigg \ (\fract+3)^3=\fract^3+t^2+9t+27\\6) \bigg \ (2-\frack)^3=8-3k+\frack^2-\frack^3](https://tex.z-dn.net/?f=%5Cdisplayctyle%5Ctt%2033.3%5C%5C1%29%20%5C%20%280.2a%2B5%29%5E3%3D0.008a%5E3%2B0.6a%5E2%2B15a%2B125%5C%5C2%29%20%5C%20%284-0.5b%29%5E3%3D64-24b%2B3b%5E2-0.125b%5E3%5C%5C3%29%20%5C%20%280.6c-5%29%5E3%3D%200.216c%5E3-5.4c%5E2%2B45c-125%5C%5C%204%29%20%5C%20%28%5Cfrac%7B1%7D%7B2%7Dd-2%29%5E3%3D%5Cfrac%7B1%7D%7B8%7Dd%5E3-%5Cfrac%7B3%7D%7B2%7Dd%5E2%2B6d-8%5C%5C5%29%20%5Cbigg%20%5C%20%28%5Cfrac%7B1%7D%7B3%7Dt%2B3%29%5E3%3D%5Cfrac%7B1%7D%7B27%7Dt%5E3%2Bt%5E2%2B9t%2B27%5C%5C6%29%20%5Cbigg%20%5C%20%282-%5Cfrac%7B1%7D%7B4%7Dk%29%5E3%3D8-3k%2B%5Cfrac%7B3%7D%7B8%7Dk%5E2-%5Cfrac%7B1%7D%7B64%7Dk%5E3)
Куб суммы: (a + b)³ = a³ + 3a²b + 3ab² + b³
Куб разности: (a - b)³ = a³ - 3a²b + 3ab² - b³
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4 апреля 2023 21:51
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