Question

1) Phân tích đa thức thành nhân tử:
a) 3a²b² - 6a²b³ + 3a²b²

b) aⁿ⁺¹ - 2a^n-1

c) 3a²b ( a+b-2) - 4ac²- 4bc²+ 8c²

d) 5a^{n (} a²-ab+1)-2a²bⁿ+2abⁿ⁺¹-2bⁿ

Answer 1

a, \(3a^2b^2-6a^2b^3+3a^2b^2\)

\(=6a^2b^2-6a^2b^3=6a^2b^2\left(1-b\right)\)

b, \(a^{n+1}-2a^{n-1}=a^2.a^{n-1}-2a^{n-1}=a^{n-1}\left(a^2-2\right)\)

c, \(3a^2b\left(a+b-2\right)-4ac^2-4bc^2+8c^2\)

\(=3a^2b\left(a+b-2\right)-4c^2\left(a+b-2\right)\)

\(=\left(3a^2b-4c^2\right)\left(a+b-2\right)\)

c, \(5a^n\left(a^2-ab+1\right)-2a^2b^n+2ab^{n+1}-2b^n\)

\(=5a^n\left(a^2-ab+1\right)-2a^2b^n+2ab^n.b-2b^n\)

\(=5a^n\left(a^2-ab+1\right)-2b^n\left(a^2-ab+1\right)\)

\(=\left(5a^n-2b^n\right)\left(a^2-ab+1\right)\)