\(F=x^6-1=\left(x^3-1\right)\left(x^3+1\right)=\left(x-1\right)\left(x+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)

\(a,=x\left(x-2\right)\\ b,=2b\left(x-3y\right)+a\left(x-3y\right)=\left(a+2b\right)\left(x-3y\right)\\ c,=x\left(x^2+2xy+y^2-4\right)=x\left[\left(x+y\right)^2-4\right]=x\left(x+y+2\right)\left(x+y-2\right)\\ d,=4-\left(x+y\right)^2=\left(2-x-y\right)\left(2+x+y\right)\\ đ,=5\left(x-y\right)\left(x+y\right)+3\left(x+y\right)^2=\left(x+y\right)\left(5x-5y+3x+3y\right)\\ =\left(x+y\right)\left(8x-2y\right)=2\left(4x-y\right)\left(x+y\right)\\ e,=3x\left(2xy-3\right)\\ b,=x\left(4x^2-4xy+y^2-4\right)=x\left[\left(2x-y\right)^2-4\right]=x\left(2x-y-2\right)\left(2x-y+2\right)\\ f,=\left(x+y\right)^2-z^2=\left(x+y-z\right)\left(x+y+z\right)\)

a,=x(x−2)b,=2b(x−3y)+a(x−3y)=(a+2b)(x−3y)c,=x(x2+2xy+y2−4)=x[(x+y)2−4]=x(x+y+2)(x+y−2)d,=4−(x+y)2=(2−x−y)(2+x+y)đ,=5(x−y)(x+y)+3(x+y)2=(x+y)(5x−5y+3x+3y)=(x+y)(8x−2y)=2(4x−y)(x+y)e,=3x(2xy−3)b,=x(4x2−4xy+y2−4)=x[(2x−y)2−4]=x(2x−y−2)(2x−y+2)f,=(x+y)2−z2=(x+y−z)(x+y+z)

\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(5+a\right)\left(x-y\right)\)

\(a^3-a^2x-ay+xy=a^2\left(a-x\right)-y\left(a-x\right)=\left(a^2-y\right)\left(a-x\right)\)

\(10x^2+10xy+5x+5y=10x\left(x+y\right)+5\left(x+y\right)=5\left(2x+1\right)\left(x+y\right)\) \(5ay-3bx+ax-15by=a\left(5y+x\right)-3b\left(5y+x\right)=\left(a-3b\right)\left(5y+x\right)\) \(x^3+x^2-x-1=x^2\left(x+1\right)-\left(x+1\right)=\left(x^2-1\right)\left(x+1\right)=\left(x+1\right)^2\left(x-1\right)\) \(2bx-3ay-6by+ax=x\left(2b+a\right)-3y\left(2b+a\right)=\left(x-3y\right)\left(2b+a\right)\)

\(x+2a\left(x-y\right)-y=\left(x-y\right)+2a\left(x-y\right)=\left(1+2a\right)\left(x-y\right)\)

a) \(2bx-3ay-6by+ax\)

\(=2b\left(x-3y\right)+a\left(-3y+x\right)\)

\(=\left(2b+a\right)\left(x-3y\right)\)

b) \(x-2ac\left(x-y\right)-y\)

\(=\left(x-y\right)-2ac\left(x-y\right)\)

\(=\left(x-y\right)\left(1-2ac\right)\)

c) \(xy^2-by^2-ax+ab+y^2-a\)

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

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

\(=\left(y^2-a\right)\left(x-b+1\right)\)

Bài 2 

\(2\left(x+3\right)-x^2-3x=0\)

\(\Leftrightarrow2x+6-x^2-3x=0\)

\(\Leftrightarrow-x^2-x+6=0\)

\(\Leftrightarrow-x^2-x=-6\)

\(\Leftrightarrow-x\left(x+1\right)=-6\)

\(\Rightarrow x=-3;x=2\)

          Vậy \(x=-3\)và  \(x=2\)

    Bạn ơi mình nha

chỗ nào k hiểu hỏi mình lại ớ 

\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)

\(=xy\left(x+y\right)+xyz+xz\left(x+z\right)+xyz+yz\left(y+z\right)\)

\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(y+z\right)\)

\(=x\left(y+z\right)\left(x+y+z\right)+yz\left(y+z\right)\)

\(=x\left(y+z\right)\left(x+y+z+yz\right)\)

\(1,2x^2-6xy+5x-15y\)

\(=2x\left(x-3y\right)+5\left(x-3y\right)\)

\(=\left(x-3y\right)\left(2x+5\right)\)

\(2,ax^{2\:}-3axy+bx-3by\)

\(=ax\left(x-3y\right)+b\left(x-3y\right)\)

\(=\left(x-3y\right)\left(ax+b\right)\)

\(3,5ax^2-3axy+3ay^2-3axy\) ( Đề sai )

Sửa : \(3ax^2-3axy+3ay^2-3axy\)

\(=3ax\left(x-y\right)+3ay\left(y-x\right)\)

\(=3ax\left(x-y\right)-3ay\left(x-y\right)\)

\(=3a\left(x-y\right)^2\)

\(4,4acx+4bcx+4ax+4bx\)

\(=4cx\left(a+b\right)+4x\left(a+b\right)\)

\(=4x\left(a+b\right)\left(c+1\right)\)

\(6,ax^{2\:}y-bx^2y-ax+bx+2a-2b\)

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

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

\(7,ax^{2\:}-bx^2-2ax+2bx-3a+3b\)

\(=x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a-b\right)\)

\(=\left(a-b\right)\left(x^2-2x-3\right)\)

\(8,ax^{2\:}-5x^2-ax+5x+a-5\)

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

\(=\left(a-5\right)\left(x^2-x+1\right)\)

\(9,ax+bx+cx-2a-2b+2c\) Đề sai

Sửa :\(ax+bx+cx-2a-2b-2c\)

\(=x\left(a+b+c\right)-2\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left(x-2\right)\)

\(10,2ax-bx+3cx-2a+b-3c\)

\(=\left(2ax-2a\right)-\left(bx-b\right)+\left(3cx-3c\right)\)

\(=2a\left(x-1\right)-b\left(x-1\right)+3c\left(x-1\right)\)

\(=\left(x-1\right)\left(2a-b+3c\right)\)

Mấy câu đề sai mk sửa chỗ nào ko đúng thì nói mk nha !

\(a,=5\left(x-y\right)+a\left(x-y\right)=\left(5+a\right)\left(x-y\right)\\ b,=a\left(x+y\right)+b\left(x+y\right)=\left(a+b\right)\left(x+y\right)\\ c,=x\left(x+1\right)+a\left(x+1\right)=\left(x+a\right)\left(x+1\right)\\ d,Sửa:x^2y+xy^2-3x-3y=xy\left(x+y\right)-3\left(x+y\right)=\left(xy-3\right)\left(x+y\right)\\ e,=xy\left(x+1\right)-\left(x+1\right)=\left(xy-1\right)\left(x+1\right)\\ f,=x^2-4=\left(x-2\right)\left(x+2\right)\\ g,=\left(x+3\right)^2-y^2=\left(x-y+3\right)\left(x+y+3\right)\\ h,=\left(x+5\right)^2-y^2=\left(x-y+5\right)\left(x+y+5\right)\\ i,=\left(x-4\right)^2-24y^2=\left(x-2\sqrt{6}y-4\right)\left(x+2\sqrt{6}y+4\right)\)

\(a,\left(2a+3\right)x-\left(2a+3\right)y+\left(2a+3\right)\)

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

\(b,\left(4x-y\right)\left(a-1\right)-\left(y-4x\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)

​\(=\left(4x-y\right)\left(a-1\right)+\left(4x-y\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)​

\(=\left(4x-y\right)\left(a-1+b-1+1-c\right)\)

\(=\left(4x-y\right)\left(a+b-c-1\right)\)

\(c,x^k+1-x^k-1\)

\(=0?!?!\)

\(d,x^m+3-x^m+1\)

\(=4\)

\(e,3\left(x-y\right)^3-2\left(x-y\right)^2\)

\(=\left(x-y\right)^2\left(3\left(x-y\right)-2\right)\)

\(=\left(x-y\right)^2\left(3x-3y-2\right)\)

\(f,81a^2+18a+1\)

\(=\left(9a\right)^2+2.9a+1\)

\(=\left(9a+1\right)^2\)

\(g,25a^2.b^2-16c^2\)

\(=\left(5ab\right)^2-\left(4c\right)^2\)

\(=\left(5ab+4c\right)\left(5ab-4c\right)\)

\(h,\left(a-b\right)^2-2\left(a-b\right)c+c^2\)

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

\(i,\left(ax+by\right)^2-\left(ax-by\right)^2\)

\(=\left(ax+by-ax+by\right)\left(ax+by+ax-by\right)\)

\(=2by.2ax\)

\(=4axby\)

\(\text{a) }\left(2a+3\right)x-\left(2a+3\right)y+\left(2a+3\right)\)

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

\(\text{b) }\left(4x-y\right)\left(a-1\right)-\left(y-4x\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)

\(=\left(4x-y\right)\left(a-1\right)+\left(4x-y\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)

\(=\left(4x-y\right)\left(a-1+b-1+1-c\right)\)

\(=\left(4x-y\right)\left(a+b-c-1\right)\)

\(\text{c) }x^k+1-x^k-1\)

\(=\left(x^k-x^k\right)+\left(1-1\right)\)

\(=0\)

\(\text{d) }x^m+3-x^m+1\)

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

\(=4\)

\(\text{e) }3\left(x-y\right)^3-2\left(x-y\right)^2\)

\(=\left(x-y\right)^2\left[3\left(x-y\right)-2\right]\)

\(=\left(x-y\right)^2\left(3x-3y-2\right)\)

\(\text{f) }81a^2+18a+1\)

\(=\left(9a\right)^2+2.9a.1+1^2\)

\(=\left(9a+1\right)^2\)

\(\text{g) }25a^2b^2-16c^2\)

\(=\left(5ab\right)^2-\left(4c\right)^2\)

\(=\left(5ab+4c\right)\left(5ab-4c\right)\)

\(\text{h) }\left(a-b\right)^2-2.\left(a-b\right).c+c^2\)

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

\(\text{i) }\left(ax+by\right)^2-\left(ax-by\right)^2\)

\(=\left(ax+by+ax-by\right)\left(ax+by-ax+by\right)\)

\(=2by.2ax\)

\(=4byax\)

a,hđt số 3 = \(\left(a^2+2a\right)^2-9\) 

b,hđt số 3=\(\left[x-\left(y-6\right)\right]\left[x+\left(y-6\right)\right]\)(đổi dấu làm ngoặc khi trước nó là dấu trừ)=\(x^2-\left(y-6\right)^2\)

a) \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)\)

\(=\left(a^2+2a\right)^2+3.\left(-3\right)\)

\(=\left(a^2+2a\right)^2-9\)

b) \(\left(x-y+6\right)\left(x+y-6\right)\)

\(=\left[x-\left(y-6\right)\right]\left[x+\left(y-6\right)\right]\)

\(=x^2-\left(y-6\right)^2\)