Question

a, 15x^4 - 5x^2 y^3 B, 9(x^4-y^4) C, 3x^2 +6xy+3y^2 D, x (a-b) -y(b-a) E,x^2 +xy-7x-7y F, x^3 +2x^2 -2x-1 Phân tích đa thức thành nhân tử

Answer 1

 

A) 
  \[
  15x^4 - 5x^2y^3 = 5x^2(3x^2 - y^3)
  \]

B) 
  \[
  x^4 - y^4 = (x^2 - y^2)(x^2 + y^2)
  \]
  \[
  x^2 - y^2 = (x - y)(x + y)
  \]
  \[
  9(x^4 - y^4) = 9(x - y)(x + y)(x^2 + y^2)
  \]

C)
  \[
  3x^2 + 6xy + 3y^2 = 3(x^2 + 2xy + y^2)
  \]
  \[
  x^2 + 2xy + y^2 = (x + y)^2
  \]
  \[
  3x^2 + 6xy + 3y^2 = 3(x + y)^2
  \]

D) 
  \[
  x(a - b) - y(b - a) = x(a - b) + y(a - b)
  \]
  \[
  x(a - b) - y(b - a) = (a - b)(x + y)
  \]

E) 
  \[
  x^2 + xy - 7x - 7y = (x^2 + xy) - (7x + 7y)
  \]
  \[
  x(x + y) - 7(x + y)
  \]
  \[
  x^2 + xy - 7x - 7y = (x + y)(x - 7)
  \]

F)
  \[
  x^3 + 2x^2 - 2x - 1 = (x^3 + 2x^2) - (2x + 1)
  \]
  \[
  x^2(x + 2) - 1(2x + 1)
  \]