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11 tháng 12 2019

\(x^8+x^4+1\)

\(=\left(x^4\right)^{^2}+2x^4+1-x^4\)

\(=\left(x^4+1\right)^2-x^4\)
\(=\left(x^4+1\right)^{^2}-\left(x^2\right)^{^2}\)
\(=\left(x^4+1-x^2\right)\left(x^4+1+x^2\right)\)

26 tháng 12 2021

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

3 tháng 8 2015

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 

1 tháng 8 2021

X^2-6+8

20 tháng 6 2016

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

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

=x^6(x^2+x+1)-x^5(x^2+x+1)+x^3(x^2+x+1)-x(x^2+x+1)+(x^2+x+1)

=(x^2+x+1)(x^6-x^5+x^3-x+1)

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

=(x^2+x+1)[x^4(x^2-x+1)-x^2(x^2-x+1)+(x^2-x+1)

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

12 tháng 10 2021

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

28 tháng 11 2021
Lol .ngudoots
3 tháng 9 2016

(x+1)(x+2)(x+3)(x+4)-8

=[(x+1).(x+4)].[(x+2).(x+3)]-8

=(x2+5x+4).(x2+5x+6)-8

Đặt (x2+5x+4)=t =>(x2+5x+6)=t+2

Thay vào biểu thức ta có:

(x2+5x+4).(x2+5x+6)-8

t.(t+2)-8

=t2+2t+1-9

=(t+1)2-32

=(x2+5x+4+1)-32

=(x2+5x+5+3).(x2+5x+5-3)

=(x2+5x+8).(x2+5x+2)

=

3 tháng 9 2016

ta làm như sau : 

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

\(\Rightarrow\left(x^2+5X+4\right)\left(x^2+5x+6\right)-8\)

Đặt \(x^2+5x+4=t\)

\(\Leftrightarrow t\left(t+2\right)-8\)

\(\Leftrightarrow t^2+2t-8\Leftrightarrow t^2+2t+1-9\)

\(\Leftrightarrow\left(t+1\right)^2-3^2\)

\(\Leftrightarrow\left(t-2\right)\left(t+4\right)\)

\(\Leftrightarrow\left(x^2+5x+2\right)\left(x^2+5x+8\right)\)

17 tháng 10 2021

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

12 tháng 8 2018

\(x^8+x^4+1\)

\(=x^4.\left(x^4+1\right)+\left(x^4+1\right)-x^4\)

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

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

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

26 tháng 2 2015

      x8 + x4 +1 = ( x+ x+ x6) - ( x7  + x+ x) + ( x+ x4  + x3 ) - (x3 - x2 - x ) + ( x+ x + 1)

                         =  x6( x2 + x + 1 ) - x5( x2 + x + 1 ) + x3( x2 + x +1 ) - x( x2 + x +1 ) + ( x2 + x +1 )

                         =  ( x2 + x +1 )( x6 - x5 + x3 - x + 1 )