a)\(81x^2-6yz-9y^2-z^2\)

\(=81x^2-\left(z-3y\right)^2\)

\(=\left(9x-z+3y\right)\left(9x+z-3y\right)\)

b)\(x^2y-x^3-9y+9x\)

\(=x^2\left(y-x\right)-9\left(y-x\right)\)

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

c)\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2-4z^2\right)\)

\(=3\left[\left(a-b\right)^2-4z^2\right]\)

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

a)\(81x^2-6yz-9y^2-z^2=\left(9x\right)^2-\left(9y^2+6yz+z^2\right)=\left(9x\right)^2-\left(3y+z\right)^2=\left(9x-3y-z\right)\left(9x+3y+z\right)\)b)\(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x^2-9\right)\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)

c)\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)

\(x^3-x^2-5x+125\)

\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)

\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)

\(=\left(x+5\right)\left(x^2-6x+25\right)\)

\(x^6-x^4-9x^3+9x^2\)

\(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)

\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)

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

\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)

\(x^4-4x^3+8x^2-16x+16\)

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

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

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

\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2-4c^2\right)\)

\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)

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

a) \(x^3-x^2-5x+125=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)=\left(x+5\right)\left(x^2-6x+25\right)\)

b) \(x^6-x^4-9x^3+9x^2=x^2\left(x^4-x^2-9x+9\right)=x^2\left[x^2\left(x-1\right)\left(x+1\right)-9\left(x-1\right)\right]=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)

c) \(x^4-4x^3+8x^2-16x+16=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)=\left(x-2\right)\left(x^3-2x^2+4x+8\right)=\left(x-2\right)\left(x^2+4\right)\left(x-2\right)=\left(x-2\right)^2\left(x^2+4\right)\)

d) \(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left(a-b-2c\right)\left(a-b+2c\right)\)

tick cho mk vs nha

đề đúng 100% chờ tí tui giải cho

a²-b²+3a+3b=(a-b)(a+b)+3(a+b)=(a+b)(a-b+3)

=(a-b).(a+b)+3.(a+b)=(a+b).(a-b+3)

a: \(=\left(m^2-2m+1\right)-\left(n^2-2np+p^2\right)\)

\(=\left(m-1\right)^2-\left(n-p\right)^2\)

\(=\left(m-1-n+p\right)\left(m-1+n-p\right)\)

b: \(=3\left(a^2-2ab+b^2-4c^2\right)\)

\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)

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

Phân tích đa thức thành nhân tử

a. 3ab ( x+ y) - 6ab ( y+ x)

   =( x + y) ( 3ab - 6ab )

     = ( x +y ) ( - 3ab)

b.7a (x - 3)+a²(x² - 9)

  =7a( x- 3) + a² ( x² - 3²)

  =7a ( x - 3 ) + a² ( x- 3 ) ( x+3 )

   = ( x- 3) . 7a + a² ( x + 3)

    = ( x- 3) ( 7a +a²x + 3a²)

c. 34 (x + y) -x -y

  = 34 ( x+ y) - ( x+y)

 =(x +y ) ( 34 - 1) = 33 ( x+ y)

  d. 25 x⁴  - 94²

     =( 5x² )² - 94²

     =( 5x² - 94 ) ( 5x²+94)

   e.( 5a - b )² - ( 2a +3b)²

      =( 5a -b -2a - 3b) (5a -b + 2a + 3b)

       =(3a - 4b) (7a+ 2b)

 k. 2² -3a - b² +3b

    =( 2² - b² ) + ( -3a +3b)

    =( 2-b) (2+b) + 3( -a +b)

mk làm đầu tiên nhớ tick cho mk nhé!!

a/ 3(a + b) + c(a + b) = (a + b)(3 + c)

b/ (a - b)² - c² = (a - b - c)(a - b + c)

3a² - 6ab + 3b² - 12c²

⁼ 3a² - 3a x 2b + 3b² - 3 x 4c²

= 3(a² -a x b +b² - 4c²)

phân tích thành nhân tử :
3a² - 6ab + 3b² - 12c²

=3(a\(^2\)-2ab+b\(^2\)-4c\(^2\))

=3[(a-b)\(^2\)-(2c)\(^2\)]

=3(a-b-2c)(a-b+2c)