Question

помогите с алгеброй, пожалуйста, все задания
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Answer 1

Вариант 1

1.

а)

$2 {m}^{3} - 18m = 2m( {m}^{2} - 9) = 2m(m - 3)(m + 3)$

б)

$7 {m}^{2} + 14mn + 7 {n}^{2} = 7( {m}^{2} + 2mn + {n}^{2} ) = 7 {(m + n)}^{2}$

в)

$6 {n}^{3} + 6 {m}^{3} = 6( {n}^{3} + {m}^{3} ) = 6(n + m)( {n}^{2} - mn + {m}^{2} )$

г)

$16 {m}^{4} - 81 {n}^{4} = (4 {m}^{2} - 9 {n}^{2} )(4 {m}^{2} + 9 {n}^{2} ) = \\ \\ = (2m - 3n)(2m + 3n)(4 {m}^{2} + 9 {n}^{2} )$

2.

$2 {x}^{3} - 8x = 0 \\ \\ 2x( {x}^{2} - 4) = 0 \\ \\ 2x(x - 2)(x + 2) = 0 \\ \\ 2x = 0 \\ x = 0 \\ \\ x - 2 = 0 \\ x = 2 \\ \\ x + 2 = 0 \\ x = - 2$

Вариант 2

1.

а)

${z}^{3} - 121z = z( {z}^{2} - 121) = z(z - 11)(z + 11)$

б)

$20 {t}^{3} + 20 {t}^{2} + 5t = 5t(4 {t}^{2} + 4t + 1) = 5t {(2t + 1)}^{2}$

в)

${z}^{4} - 27z {y}^{3} = z( {z}^{3} - 27 {y}^{3} ) = z(z - 3y)( {z}^{2} + 3yz + 9 {y}^{2} )$

г)

${t}^{2} - {y}^{2} + 2t - 2y = (t - y)(t + y) + 2(t - y) = (t - y)(t + y + 2)$

2.

${x}^{3} + 2 {x}^{2} + x = 0 \\ \\ x( {x}^{2} + 2x + 1) = 0 \\ \\ x {(x + 1)}^{2} = 0 \\ \\ x = 0 \\ \\ x + 1 = 0 \\ x = - 1$