Предмет: Алгебра,
автор: nnnnnnnnnnnnnn3
Помогите срочно!!!
Пожалуйста)
Приложения:
![](https://files.topotvet.com/i/e24/e24dfe253255ed58f81c3a7d5e70b5f6.png)
Ответы
Автор ответа:
1
1.
1)
![{b}^{3} - 8 {c}^{2} = (b - 2c)( {b}^{2} + 2bc + 4 {c}^{2} ) {b}^{3} - 8 {c}^{2} = (b - 2c)( {b}^{2} + 2bc + 4 {c}^{2} )](https://tex.z-dn.net/?f=+%7Bb%7D%5E%7B3%7D++-+8+%7Bc%7D%5E%7B2%7D++%3D+%28b+-+2c%29%28+%7Bb%7D%5E%7B2%7D++%2B+2bc+%2B+4+%7Bc%7D%5E%7B2%7D+%29)
2)
![49 {x}^{2} y - {y}^{3} = y(49 {x}^{2} - {y}^{2} ) = y(7x - y)(7x + y) 49 {x}^{2} y - {y}^{3} = y(49 {x}^{2} - {y}^{2} ) = y(7x - y)(7x + y)](https://tex.z-dn.net/?f=49+%7Bx%7D%5E%7B2%7D+y+-++%7By%7D%5E%7B3%7D++%3D+y%2849+%7Bx%7D%5E%7B2%7D++-++%7By%7D%5E%7B2%7D+%29+%3D+y%287x+-+y%29%287x+%2B+y%29)
3)
![- 7 {a}^{2} + 14a - 7 = - 7( {a}^{2} - 2a + 1) = - 7({a - 1})^{2} - 7 {a}^{2} + 14a - 7 = - 7( {a}^{2} - 2a + 1) = - 7({a - 1})^{2}](https://tex.z-dn.net/?f=+-+7+%7Ba%7D%5E%7B2%7D++%2B+14a+-+7+%3D++-+7%28+%7Ba%7D%5E%7B2%7D++-+2a+%2B+1%29+%3D++-+7%28%7Ba+-+1%7D%29%5E%7B2%7D+)
4)
![5ab - 15b - 5a + 15 = 5a(b - 1) - 15(b - 1) = (5a - 15)(b - 1) = 5(a - 3)(b - 1) 5ab - 15b - 5a + 15 = 5a(b - 1) - 15(b - 1) = (5a - 15)(b - 1) = 5(a - 3)(b - 1)](https://tex.z-dn.net/?f=5ab+-+15b+-+5a+%2B+15+%3D+5a%28b+-+1%29+-+15%28b+-+1%29+%3D+%285a+-+15%29%28b+-+1%29+%3D+5%28a+-+3%29%28b+-+1%29)
5)
![{a}^{4} - 1 = ( {a}^{2} - 1)( {a}^{2} + 1) = (a - 1)(a + 1)( {a}^{2} + 1) {a}^{4} - 1 = ( {a}^{2} - 1)( {a}^{2} + 1) = (a - 1)(a + 1)( {a}^{2} + 1)](https://tex.z-dn.net/?f=+%7Ba%7D%5E%7B4%7D++-+1+%3D+%28+%7Ba%7D%5E%7B2%7D++-+1%29%28+%7Ba%7D%5E%7B2%7D++%2B+1%29+%3D+%28a+-+1%29%28a+%2B+1%29%28+%7Ba%7D%5E%7B2%7D++%2B+1%29)
2.
![(3a + 1)(9 {a}^{2} - 3a + 1) = ( {3a)}^{3} + ( {1})^{3} = 27 {a}^{3} + 1 = 27 \times \frac{1}{27} + 1 = 1 + 1 = 2 (3a + 1)(9 {a}^{2} - 3a + 1) = ( {3a)}^{3} + ( {1})^{3} = 27 {a}^{3} + 1 = 27 \times \frac{1}{27} + 1 = 1 + 1 = 2](https://tex.z-dn.net/?f=%283a+%2B+1%29%289+%7Ba%7D%5E%7B2%7D++-+3a+%2B+1%29+%3D+%28+%7B3a%29%7D%5E%7B3%7D+%2B+%28+%7B1%7D%29%5E%7B3%7D++%3D+27+%7Ba%7D%5E%7B3%7D++%2B+1+%3D+27+%5Ctimes++%5Cfrac%7B1%7D%7B27%7D++%2B+1+%3D+1+%2B+1+%3D+2)
3.
1)
![a + b + {a}^{2} - {b}^{2} = 1(a + b) + (a + b)(a - b) = (a + b)(1 + a - b) a + b + {a}^{2} - {b}^{2} = 1(a + b) + (a + b)(a - b) = (a + b)(1 + a - b)](https://tex.z-dn.net/?f=a+%2B+b+%2B++%7Ba%7D%5E%7B2%7D++-++%7Bb%7D%5E%7B2%7D++%3D+1%28a+%2B+b%29+%2B+%28a+%2B+b%29%28a+-+b%29+%3D+%28a+%2B+b%29%281+%2B+a+-+b%29)
2)
![9 {a}^{2} - 6ab + {b}^{2} - 16 =(3a - b)^{2} - 16 = (3a - b - 4)(3a - b + 4) 9 {a}^{2} - 6ab + {b}^{2} - 16 =(3a - b)^{2} - 16 = (3a - b - 4)(3a - b + 4)](https://tex.z-dn.net/?f=9+%7Ba%7D%5E%7B2%7D++-+6ab+%2B++%7Bb%7D%5E%7B2%7D++-+16+%3D%283a+-+b%29%5E%7B2%7D++-+16+%3D+%283a+-+b+-+4%29%283a+-+b+%2B+4%29)
3)
![{x}^{3} {y}^{2} - {x}^{3} - x {y}^{2} + x = {x}^{3} ( {y}^{2} - 1) - x( {y}^{2} - 1) = x(x - 1)(x + 1)(y - 1)(y + 1) {x}^{3} {y}^{2} - {x}^{3} - x {y}^{2} + x = {x}^{3} ( {y}^{2} - 1) - x( {y}^{2} - 1) = x(x - 1)(x + 1)(y - 1)(y + 1)](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B3%7D++%7By%7D%5E%7B2%7D++-++%7Bx%7D%5E%7B3%7D++-+x+%7By%7D%5E%7B2%7D++%2B+x+%3D++%7Bx%7D%5E%7B3%7D+%28+%7By%7D%5E%7B2%7D++-+1%29+-+x%28+%7By%7D%5E%7B2%7D++-+1%29+%3D+x%28x+-+1%29%28x+%2B+1%29%28y+-+1%29%28y+%2B+1%29)
4)
![1 - {x}^{2} + 4xy - 4 {y}^{2} = 1 - (x - 2y)^{2} = (1 - x + 2y)(1 + x - 2y) 1 - {x}^{2} + 4xy - 4 {y}^{2} = 1 - (x - 2y)^{2} = (1 - x + 2y)(1 + x - 2y)](https://tex.z-dn.net/?f=1+-++%7Bx%7D%5E%7B2%7D++%2B+4xy+-+4+%7By%7D%5E%7B2%7D+%3D++1+-+%28x+-+2y%29%5E%7B2%7D++%3D+%281+-+x+%2B+2y%29%281+%2B+x+-+2y%29)
4.
1)
![2 {x}^{3} - 50x = 0 \\ 2x(x - 5)(x + 5) = 0 \\ x = 0 \\ x = 5 \\ x= - 5 2 {x}^{3} - 50x = 0 \\ 2x(x - 5)(x + 5) = 0 \\ x = 0 \\ x = 5 \\ x= - 5](https://tex.z-dn.net/?f=2+%7Bx%7D%5E%7B3%7D++-+50x+%3D+0+%5C%5C+2x%28x+-+5%29%28x+%2B+5%29+%3D+0+%5C%5C+x+%3D+0+%5C%5C+x+%3D+5+%5C%5C+x%3D++-+5)
2)
![16 {x}^{3} + 8 {x}^{2} + x = 0 \\ x(4x + 1)^{2} = 0 \\ x = 0 \\ x = - \frac{1}{4} 16 {x}^{3} + 8 {x}^{2} + x = 0 \\ x(4x + 1)^{2} = 0 \\ x = 0 \\ x = - \frac{1}{4}](https://tex.z-dn.net/?f=16+%7Bx%7D%5E%7B3%7D++%2B+8+%7Bx%7D%5E%7B2%7D++%2B+x+%3D+0+%5C%5C+x%284x+%2B+1%29%5E%7B2%7D++%3D+0+%5C%5C+x+%3D+0+%5C%5C+x+%3D++-++%5Cfrac%7B1%7D%7B4%7D+)
3)
![{x}^{3} + 2 {x}^{2} - 36x - 72 = 0 \\ {x}^{2} (x + 2) - 36(x + 2) = 0 \\ (x - 6)(x + 6)(x + 2) = 0 \\ x = 6 \\ x = - 6 \\ x = - 2 {x}^{3} + 2 {x}^{2} - 36x - 72 = 0 \\ {x}^{2} (x + 2) - 36(x + 2) = 0 \\ (x - 6)(x + 6)(x + 2) = 0 \\ x = 6 \\ x = - 6 \\ x = - 2](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B3%7D++%2B+2+%7Bx%7D%5E%7B2%7D++-+36x+-+72+%3D+0+%5C%5C++%7Bx%7D%5E%7B2%7D+%28x+%2B+2%29+-+36%28x+%2B+2%29+%3D+0+%5C%5C+%28x+-+6%29%28x+%2B+6%29%28x+%2B+2%29+%3D+0+%5C%5C+x+%3D+6+%5C%5C+x+%3D++-+6+%5C%5C+x+%3D++-+2)
5.
![\frac{ {3}^{9} - {4}^{3} }{23} = \frac{( {3}^{3} - 4)( {3}^{6} + 4 \times {3}^{3} + 16) }{23} = \frac{23(729 +108 + 16) }{23} = 853 \frac{ {3}^{9} - {4}^{3} }{23} = \frac{( {3}^{3} - 4)( {3}^{6} + 4 \times {3}^{3} + 16) }{23} = \frac{23(729 +108 + 16) }{23} = 853](https://tex.z-dn.net/?f=+%5Cfrac%7B+%7B3%7D%5E%7B9%7D+-++%7B4%7D%5E%7B3%7D++%7D%7B23%7D++%3D++%5Cfrac%7B%28+%7B3%7D%5E%7B3%7D+-+4%29%28+%7B3%7D%5E%7B6%7D+%2B+4+%5Ctimes++%7B3%7D%5E%7B3%7D++%2B+16%29++%7D%7B23%7D++%3D++%5Cfrac%7B23%28729+%2B108+%2B+16%29+%7D%7B23%7D++%3D+853)
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