Question

Разложите на множители:

Answer 1

5) 12a²b³ - 18a⁵b² = 6a²b²(2b - 3a³)

6) 8x + 8y - ax - ay = (8x + 8y) - (ax + ay) = 8(x + y) - a(x + y) = (x + y)(8 - a)

3) (b² - 7)² - b(b² - 7) = (b² - 7)(b² - 7) - b(b² - 7) = (b² - 7)(b² - 7 - b)

4) 8m⁷ - 6m²n - 12m⁵n³ + 9n⁴ = (8m⁷ - 6m²n) - (12m⁵n³ - 9n⁴) =

= 2m²(4m⁵ - 3n) - 3n³(4m⁵ - 3n) = (4m⁵ - 3n)(2m² - 3n³)

Answer 2

$12a^2b^3-18a^5b^2=6a^2b^2\cdot (2b-3a^3)\\\\\\8x+8y-ax-ay=8(x+y)-a(x+y)=(x+y)(8-a)\\\\\\(b^2-7)^2-b(b^2-7)=(b^2-7)\cdot (b^2-7-b)=(b-\sqrt7)(b+\sqrt7)(b^2-b-7)\\\\\\8m^7-6m^2n-12m^5n^3+9n^4=2m^2(4m^5-3n)-3n^3(4m^5-3n)=\\\\=(4m^5-3n)(2m^2-3n^3)$