Разложите на множители 1)a^3-27+3a^2-9a2)b^3+125+2b+103)3x+6y-x^3-8y^3. Created by ucenikthl. algebra-ru

Разложите на множители 1)a^3-27+3a^2-9a2)b^3+125+2b+103)3x+6y-x^3-8y^3...

ucenikthl @ucenikthl

November 2021 1 18 Report

Разложите на множители
1)a^3-27+3a^2-9a
2)b^3+125+2b+10
3)3x+6y-x^3-8y^3

Answers & Comments

xERISx

Verified answer

1) a³ - 27 + 3a² - 9a = (a³ - 3³) + 3a(a - 3) =
= (a - 3)(a² + 3a + 3²) + 3a(a - 3) = (a - 3)(a² + 3a + 9 + 3a) =
= (a - 3)(a² + 6a + 9) = (a - 3)(a + 3)²

2) b³ + 125 + 2b + 10 = b³ + 5³ + 2(b + 5) =
= (b + 5)(b² - 5b + 5²) + 2(b + 5) = (b + 5)(b² - 5b + 25 + 2) =
= (b + 5)(b² - 5b + 27)

3) 3x + 6y - x³ - 8y³ = 3(x + 2y) - (x³ + (2y)³) =
= 3(x + 2y) - (x + 2y)(x² - 2xy + (2y)²) = (x + 2y)(3 - (x² - 2xy + 4y²)) =
= (x + 2y)(3 - x² + 2xy - 4y²)
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Использованы формулы суммы и разности кубов
c³ + d³ = (c + d)(c² - cd + d²)
c³ - d³ = (c - d)(c² + cd - d²)

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