a,
[tex]\dpi{100} 4x^2-4x-9y^2+1\\=4x^2-4x+1-9y^2\\=(2x-1)^2-(3y)^2\\=(2x-1+3y)(2x-1-3y)[/tex]
b,
[tex]\dpi{100} x^2-10x+25=(x-5)^2[/tex]
c,
[tex]\dpi{100} -x^2+\frac{1}{4}\\=\frac{1}{4}-x^2\\=(\frac{1}{2}+x)(\frac{1}{2}-x)[/tex]
d,
[tex]\dpi{100} x^3+x^2y-x^2z-xyz\\=x^2(x+y)-xz(x+y)\\=(x^2-xz)(x+y)\\=x(x-z)(x+y)[/tex]
e,
Đề phải thế này chớ [tex]\dpi{100} x^2+2xy-xz-yz+y^2[/tex]
f,
[tex]\dpi{100} x^3+3x^2+3x-8y^3+1\\=x^3+3x^2+3x+1-8y^3\\=(x+1)^3-(2y)^3\\=(x+1-2y)[(x+1)^2+2y(x+1)+4y^2]\\=(x+1-2y)(x^2+2x+1+2xy+2y+4y^2)[/tex]
g,
[tex]\dpi{100} 4x^2+8x-5\\=4x^2-2x+10x-5\\=2x(2x-1)+5(2x-1)\\=(2x-1)(2x+5)[/tex]
h,
[tex]\dpi{100} (x+1)(x+2)(x+3)(x+4)-24\\=(x^2+x+2x+2)(x^2+3x+4x+12)\\=(x^2+3x+2)(x^2+7x+12)-24\\=x^4+7x^3+12x^2+3x^3+21x^2+36x+2x^2+14x+24-24\\=x^4+10x^3+35x^2+50x\\=x(x^3+10x^2+35x+50)\\=x(x^3+5x^2+5x^2+25x+10x+50)\\=x[x^2(x+5)+5x(x+5)+10(x+5)]\\=x(x+5)(x^2+5x+10)[/tex]
i,
[tex]\dpi{100} 2x^2-x+y-2y^2\\=2x^2-2y^2-x+y\\=2(x^2-y^2)-(x-y)\\=2(x+y)(x-y)-(x-y)\\=(x-y)[2(x+y)-1]=(x+y)(2x+2y-1)[/tex]
k, Sai đề