Bài 1 :

\(x^2-6x+8=x^2-2x-4x+8=x\left(x-2\right)-4\left(x-2\right)=\left(x-4\right)\left(x-2\right)\)

Bài 2 :

 \(x^8+x^7+1=x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1-x^6-x^5-x^4-x^3-x^2-x\)

\(=x^6\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)+x^2+x+1-x^4\left(x^2+x+1\right)-x\left(x^2+x+1\right)\)

=\(\left(x^2+x+1\right)\left(x^6+x^3+1-x^4-x\right)\)

Tick đúng nha 

X^2-6+8

\(-8x^3+1=1^3-\left(2x\right)^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)

`#3107.101107`

`(x^2x^2 - 8)^2 - 1`

`= (x^4 - 8)^2 - 1^2`

`= (x^4 - 8 - 1)(x^4 - 8 + 1)`

`= (x^4 - 9)(x^4 - 7)`

`= [ (x^2)^2 - 3^2](x^4 - 7)`

`= (x^2 - 3)(x^2 + 3)(x^4 - 7)`

\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)

x 16 + x 8 − 2 = ( x 8 ) 2 + x 8 − 2 = ( x 8 − 1 ) ( x 8 + 2 ) = ( x 4 − 1 ) ( x 4 + 1 ) ( x 8 + 2 ) = ( x 2 − 1 ) ( x 2 + 1 ) ( x 4 + 1 ) ( x 8 + 2 ) = ( x − 1 ) ( x + 1 ) ( x 2 + 1 ) ( x 4 + 1 ) ( x 8 + 2 )

\((x^2y^2-8)^2-1\\=(x^2y^2-8)^2-1^2\\=(x^2y^2-8-1)(x^2y^2-8+1)\\=(x^2y^2-9)(x^2y^2-7)\\=[(xy)^2-3^2](x^2y^2-7)\\=(xy-3)(xy+3)(x^2y^2-7)\)

`#3107.101107`

`(x^2y^2 - 8)^2 - 1`

`= (x^2y^2 - 8)^2 - 1^2`

`= (x^2y^2 - 8 - 1)(x^2y^2 - 8 + 1)`

`= (x^2y^2 - 9)(x^2y^2 - 7)`

`= (x^2y^2 - 3^2)(x^2y^2 - 7)`

`= (xy - 3)(xy + 3)(x^2y^2 - 7)`

____

Sử dụng hđt:

`A^2 - B^2 = (A - B)(A + B).`

\(x^2-6x+8\)

\(=\left(x^2-6x+9\right)-1\)

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

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

\(=\left(x-4\right)\left(x-2\right)\)

(Tíck cho mìk vs nha!)

cách 2:

x²  -6x +8 = x² -2x -4x+8= x(x-2) -4(x-2)

= (x-2)(x-4)

\(A=\left(x-1\right)\left(x-2\right)\left(x+7\right)\left(x+8\right)+8\)

\(A=\left[\left(x-1\right)\left(x+7\right)\right]\left[\left(x-2\right)\left(x+8\right)\right]+8\)

\(A=\left(x^2+6x-7\right)\left(x^2+6x-16\right)+8\)

Đặt \(q=x^2+6x-7\)ta có :

\(A=q\left(q-9\right)+8\)

\(A=q^2-9q+8\)

\(A=q^2-q-8q+8\)

\(A=q\left(q-1\right)-8\left(q-1\right)\)

\(A=\left(q-1\right)\left(q-8\right)\)

Thay \(q=x^2+6x-7\)vào A ta được :

\(A=\left(x^2+6x-7-1\right)\left(x^2+6x-7-8\right)\)

\(A=\left(x^2+6x-8\right)\left(x^2+6x-15\right)\)

 [ (x+2)^2 + 5]^2 +3x^3 + 14x^2 + 24x 
= (x+2)^4 + 8[(x+2)]^2 + 16 + (3x^2).(x+2) + 8x(x+2) +8x 
=(x+2).[(x+2)^3 +8(x+2) + 3x^2 +8x +8 ] 
=(x+2).[x^3 + 9x^2 + 28x +32 ] 
=(x+2).(x+4).(x^2 +5x +8)

các bạn ơi làm ơn giải hộ mình bài này mình đang cần rất rất gấp

Bạn kiểm tra lại đề đi nhé (lớp 8 chưa học số vô tỉ, căn)

Nếu đề bạn đúng thì dùng công thức lớp 9 (cái này bạn tự tìm hiểu chứ mình cũng không nhớ).