Question

[Anh Thu]

 Bài 8: Phân tích đa thức sau thành nhân tử

  1)(x+y)^2-9x^2

  2)(3x-1)^2-16

  3)4x^2-(x^2+1)^2

  4)(2x+1)^2 -(x-1)^2

  5)(x+1)^4 - (x-1)^4

  6)25(x-y)^2 - 16(x+y)^2

  7) (x^2+xy)^2 - (y^2 + xy)^2

  8)(x^2 +4y^2-20)^2 -16(xy-4)^2

Answer 1

[Nguyễn Lê Phước Thịnh]

1: =(x+y-3x)(x+y+3x)

=(-2x+y)(4x+y)

2: =(3x-1-4)(3x-1+4)

=(3x+3)(3x-5)

=3(x+1)(3x-5)

3: =(2x)^2-(x^2+1)^2

=-[(x^2+1)^2-(2x)^2]

=-(x^2+1-2x)(x^2+1+2x)

=-(x-1)^2(x+1)^2

4: =(2x+1+x-1)(2x+1-x+1)

=3x(x+2)

5: =[(x+1)^2-(x-1)^2][(x+1)^2+(x-1)^2]

=(2x^2+2)*4x

=8x(x^2+1)

6: =(5x-5y)^2-(4x+4y)^2

=(5x-5y-4x-4y)(5x-5y+4x+4y)

=(x-9y)(9x-y)

7: =(x^2+xy+y^2+xy)(x^2+xy-y^2-xy)

=(x^2+2xy+y^2)(x^2-y^2)

=(x+y)^3*(x-y)

8: =(x^2+4y^2-20-4xy+16)(x^2+4y^2-20+4xy-16)

=[(x-2y)^2-4][(x+2y)^2-36]

=(x-2y-2)(x-2y+2)(x+2y-6)(x+2y+6)