Question

phân tích thành nhân tử

a) c² + bc - a² - ab

b) x³ - 2x² - x + 2

c) x³ - 3x² + 9x - 27

d) (x² + x)² + 4x² + 4x + 4

Answer 1

\(c^2+bc-a^2-ab=\left(c^2-a^2\right)+\left(bc-ab\right)=\left(a+c\right)\left(c-a\right)+b\left(c-a\right)=\left(a+b+c\right)\left(c-a\right)\) \(x^3-3x^2+9x-27=\left(x^3-3x^2\right)+\left(9x-27\right)=x^2\left(x-3\right)+9\left(x-3\right)=\left(x^2+9\right)\left(x-3\right)\)\(\left(x^2+x\right)^2+4x^2+4x+4=\left(x^2+x\right)^2+4\left(x^2+x\right)+4=\left(x^2+x+2\right)^2\)

\(x^3-2x^2-x+2=\left(x^3-2x^2\right)-\left(x-2\right)=x^2\left(x-2\right)-\left(x-2\right)=\left(x^2-1\right)\left(x-2\right)=\left(x-2\right)\left(x-1\right)\left(x+1\right)\)

Answer 2

a, \(c^2+bc-a^2-ab\)

=>\(\left(c^2-a^2\right)+\left(bc-ab\right)\)

=>\(\left(c+a\right)\left(c-a\right)\) +b(c-a)

=>(c-a)(a+b+c)

b,\(x^3-2x^2-x+2\)

=>(\(x^3-2x^2\))-(x-2)

=>\(x^2\)(x-2)-(x-2)

=>(x-2)(\(x^2\)-1)