Question

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 .

Answer 1

▪1)

${x}^{3} - 1 = (x - 1)( {x}^{2} + x + 1)$

▪2)

$27 + {a}^{3} = {3}^{3} + {a}^{3} = (3 + a)(9 - 3a + {a}^{2} )$

▪3)

$216 - {y}^{3} = {6}^{3} - {y}^{3} = (6 - y)(36 + 6y + {y}^{2} )$

▪4)

$8 {a}^{3} + {b}^{3} = {(2a)}^{3} + {b}^{3} = (2a + b)(4 {a}^{2} - 2ab + {b}^{2} )$

▪5)

${a}^{6} - 8 = {( {a}^{2}) }^{3} - {2}^{3} = ( {a}^{2} - 2)( {a}^{4} + 2 {a}^{2} + 4)$

▪6)

${a}^{3} {b}^{3} - {c}^{3} = (ab - c)( {a}^{2} {b}^{2} + abc + {c}^{2} )$

▪7)

${a}^{3} - {b}^{15} {c}^{18} = {a}^{3} - {( {b}^{5} {c}^{6} )}^{3} = (a - {b}^{5} {c}^{6})( {a}^{2} + a{b}^{5} {c}^{6} + {b}^{10} {c}^{12})$

▪8)

$125 {c}^{3} {d}^{3} + 0.008 {b}^{3} = {(5cd)}^{3} + {(0.2b)}^{3} = (5cd + 0.2b)(25 {c}^{2} {d}^{2} - bcd + 0.04 {b}^{2} )$

▪9)

$64729 {x}^{3} - 271000 {y}^{6} = ....$