Разложите на множители: 1) x 3 − 1 ; 2) 27 + a 3 ; 3) 216 − y 3 ; 4) 1 8 a 3 + b 3 ; 5) a 6 − 8 ; 6) a 3 b 3 − c 3 ; 7) a 3 − b 15 c 18 ; 8) 125 c 3 d 3 + 0 , 008 b 3 ; 9) 64 729 x 3 − 27 1000 y 6 .
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▪1)
![{x}^{3} - 1 = (x - 1)( {x}^{2} + x + 1) {x}^{3} - 1 = (x - 1)( {x}^{2} + x + 1)](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B3%7D++-+1+%3D+%28x+-+1%29%28+%7Bx%7D%5E%7B2%7D+%2B++x+%2B+1%29)
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![27 + {a}^{3} = {3}^{3} + {a}^{3} = (3 + a)(9 - 3a + {a)}^{2} 27 + {a}^{3} = {3}^{3} + {a}^{3} = (3 + a)(9 - 3a + {a)}^{2}](https://tex.z-dn.net/?f=27+%2B++%7Ba%7D%5E%7B3%7D++%3D++%7B3%7D%5E%7B3%7D++%2B++%7Ba%7D%5E%7B3%7D+%3D++%283+%2B+a%29%289+-+3a+%2B++%7Ba%29%7D%5E%7B2%7D+)
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![216 - {y}^{3} = {6}^{3} - {y}^{3} = (6 - y)(36 + 6y + {y}^{2} ) 216 - {y}^{3} = {6}^{3} - {y}^{3} = (6 - y)(36 + 6y + {y}^{2} )](https://tex.z-dn.net/?f=216+-++%7By%7D%5E%7B3%7D++%3D++%7B6%7D%5E%7B3%7D++-++%7By%7D%5E%7B3%7D++%3D+%286+-+y%29%2836+%2B+6y+%2B++%7By%7D%5E%7B2%7D+%29)
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![8 {a}^{3} + {b}^{3} = {(2a)}^{3} + {b}^{3} = (2a + b)(4 {a}^{2} - 2ab + {b}^{2} ) 8 {a}^{3} + {b}^{3} = {(2a)}^{3} + {b}^{3} = (2a + b)(4 {a}^{2} - 2ab + {b}^{2} )](https://tex.z-dn.net/?f=8+%7Ba%7D%5E%7B3%7D++%2B++%7Bb%7D%5E%7B3%7D++%3D++%7B%282a%29%7D%5E%7B3%7D++%2B++%7Bb%7D%5E%7B3%7D++%3D+%282a+%2B+b%29%284+%7Ba%7D%5E%7B2%7D++-+2ab+%2B++%7Bb%7D%5E%7B2%7D+%29)
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![{a}^{6} - 8 = {( {a}^{2}) }^{3} - {2}^{3} = ( {a}^{2} - 2)( {a}^{4} + 2 {a}^{2} + 4) {a}^{6} - 8 = {( {a}^{2}) }^{3} - {2}^{3} = ( {a}^{2} - 2)( {a}^{4} + 2 {a}^{2} + 4)](https://tex.z-dn.net/?f=+%7Ba%7D%5E%7B6%7D++-+8+%3D++%7B%28+%7Ba%7D%5E%7B2%7D%29+%7D%5E%7B3%7D++-++%7B2%7D%5E%7B3%7D++%3D+%28+%7Ba%7D%5E%7B2%7D++-+2%29%28+%7Ba%7D%5E%7B4%7D++%2B+2+%7Ba%7D%5E%7B2%7D++%2B+4%29)
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![{a}^{3} {b}^{3} - {c}^{3} = (ab - c)( {a}^{2} {b}^{2} + abc + {c}^{2} ) {a}^{3} {b}^{3} - {c}^{3} = (ab - c)( {a}^{2} {b}^{2} + abc + {c}^{2} )](https://tex.z-dn.net/?f=+%7Ba%7D%5E%7B3%7D++%7Bb%7D%5E%7B3%7D++-++%7Bc%7D%5E%7B3%7D++%3D+%28ab+-+c%29%28+%7Ba%7D%5E%7B2%7D++%7Bb%7D%5E%7B2%7D++%2B+abc+%2B++%7Bc%7D%5E%7B2%7D+%29)
▪7)
![{a}^{3} - {b}^{15} {c}^{18} = {a}^{3} - {( {b}^{5} {c}^{6} )}^{3} = (a - {b}^{5} {c}^{6})( {a}^{2} + a{b}^{5} {c}^{6} + {b}^{10} {c}^{12}) {a}^{3} - {b}^{15} {c}^{18} = {a}^{3} - {( {b}^{5} {c}^{6} )}^{3} = (a - {b}^{5} {c}^{6})( {a}^{2} + a{b}^{5} {c}^{6} + {b}^{10} {c}^{12})](https://tex.z-dn.net/?f=+%7Ba%7D%5E%7B3%7D++-++%7Bb%7D%5E%7B15%7D++%7Bc%7D%5E%7B18%7D++%3D+%7Ba%7D%5E%7B3%7D++-++%7B%28+%7Bb%7D%5E%7B5%7D++%7Bc%7D%5E%7B6%7D+%29%7D%5E%7B3%7D++%3D+%28a+-+%7Bb%7D%5E%7B5%7D++%7Bc%7D%5E%7B6%7D%29%28+%7Ba%7D%5E%7B2%7D++%2B+a%7Bb%7D%5E%7B5%7D++%7Bc%7D%5E%7B6%7D+%2B+%7Bb%7D%5E%7B10%7D++%7Bc%7D%5E%7B12%7D%29)
▪8)
![125 {c}^{3} {d}^{3} + 0.008 {b}^{3} = {(5cd)}^{3} + {(0.2b)}^{3} = (5cd + 0.2b)(25 {c}^{2} {d}^{2} - bcd + 0.04 {b}^{2} ) 125 {c}^{3} {d}^{3} + 0.008 {b}^{3} = {(5cd)}^{3} + {(0.2b)}^{3} = (5cd + 0.2b)(25 {c}^{2} {d}^{2} - bcd + 0.04 {b}^{2} )](https://tex.z-dn.net/?f=125+%7Bc%7D%5E%7B3%7D++%7Bd%7D%5E%7B3%7D++%2B+0.008+%7Bb%7D%5E%7B3%7D++%3D++%7B%285cd%29%7D%5E%7B3%7D++%2B++%7B%280.2b%29%7D%5E%7B3%7D++%3D+%285cd+%2B+0.2b%29%2825+%7Bc%7D%5E%7B2%7D++%7Bd%7D%5E%7B2%7D++-+bcd+%2B+0.04+%7Bb%7D%5E%7B2%7D+%29)
▪9)
![64729 {x}^{3} - 271000 {y}^{6} = .... 64729 {x}^{3} - 271000 {y}^{6} = ....](https://tex.z-dn.net/?f=64729+%7Bx%7D%5E%7B3%7D++-+271000+%7By%7D%5E%7B6%7D++%3D+....)
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