Question

Phân tích đa thức thành nhân tử

a, 5a^2 - 5b^2

b,2ab^2 - a^2b - b^3

c, a^3+ a^2b - ab^2 - b^3

d, x^3 + x^2 - 4x - 4

e, x^4 - 4x^3 + 4x^2

f, x^3 - x^2 - x - 1

Answer 1

a, \(5a^2-5b^2=5\left(a^2-b^2\right)=5\left(a+b\right)\left(a-b\right)\)

b, \(2ab^2-a^2b-b^3=b\left(2ab-a^2b-b^2\right)=-b\left(a^2-2ab+b^2\right)\)

\(=-b\left(a-b\right)^2\)

Answer 2

a) 5a² - 5b² = 5(a²-b²) = ( a+b) (a-b)

b) 2ab² - a²b - b³ = b ( 2ab-a²-b² ) = -b (a²-2ab+b²) = -b (a-b)²

Answer 3

c: \(=\left(a-b\right)\left(a^2+ab+b^2\right)+ab\left(a-b\right)\)

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

d: \(=x^2\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\)

e: \(=x^2\left(x^2-4x+4\right)=x^2\left(x-2\right)^2\)