a/ \(P+Q=\left(x^2y+x^3-xy^2+3\right)+\left(x^3+xy^2-xy-6\right)\)

\(=x^2y+x^3-xy^2+3+x^3+xy^2-xy-6\)

\(=\left(x^3+x^3\right)+\left(xy^2-xy^2\right)+\left(3-6\right)+x^2y-xy\)

\(=2x^3+x^2y-xy-3\)

b/ \(M+N=\left(x^2y+0,5xy^3-7,5x^3y^2+x^3\right)+\)

\(\left(3xy^3-x^2y+5,5x^3y^2\right)\)

\(=x^2y+0,5xy^3-7,5x^3y^2+x^3+3xy^3-x^2y+5,5x^3y^2\)

\(=\left(x^2y-x^2y\right)+\left(0,5xy^3+3xy^3\right)+\left(5,5x^3y^2-7,5x^3y^2\right)+x^3\)

\(=3,5xy^3-2x^3y^2+x^3\)

\(A=5x^2y-xy^2+4xy+6\)             bậc : 3

a)\(B=-5x^2y+xy^2-4xy-6\)

b)\(=>C=-2xy+1-5x^2y+xy^2-4xy-6\)

\(C=-5x^2y+xy^2-6xy-5\)

Ta có A + 2B = (x2y - xy2 + 3x2) + 2(x2y + xy2 - 2x2 - 1)

= x2y - xy2 + 3x2 + 2x2y + 2xy2 - 4x2 - 2

= 3x2y + xy2 - x2 - 2. Chọn C

khó quá

Đề sai r bn, nếu x,y thay đổi thì tổng biểu thức cũng thay đổi

-Đề sai.

\(A=4x^2y+\dfrac{14}{15}xy^2-2xy-\dfrac{2}{3}\)            bậc : 3

\(B=2xy^2z-1\)                  bậc :4

+ Thu gọn :

\(A=4x^2y+\dfrac{14}{15}xy^2-2xy-\dfrac{2}{3}\)

\(B=2xy^2z-1\)

+ Bậc

Đa thức \(A\) có 4 hạng tử :

  \(4x^2y\) có bậc \(3\)

 \(\dfrac{14}{15}xy^2\) có bậc \(3\)

 \(-2xy\) có bậc \(2\)

 \(-\dfrac{2}{3}\) có bậc \(0\)

Đa thức \(B\) có \(2\) hạng tử :

   \(2xy^2z\) có bậc \(4\)

   \(-1\) có bậc \(0\)

`a)(x-1)(x^2+x+1)`

`=x^3+x^2+x-x^2-x-1`

`=x^3-1`

`b)(x^3+x^2y+xy^2+y^3)(x-y)`

`=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4`

`=x^4-y^4`

a) VT`=(x-1)(x^2+x+1)`

`=x^3 +x^2 +x -x^2-x-1 `

`=x^3-1=` VP.

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

`=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4`

`=x^4-y^4=` VP.

a, `(8x^3-4x^2): 4x -(4x^2-5x) : 2x + (2x)^2`

`=4x (2x^2-x) : 4x - 2x(2x-5/2 ) :2x + 4x^2`

`=2x^2-x-2x+5/2+4x^2`

`=6x^2-3x+5/2`

b, `(3x^3-x^2y) :x^2 -(xy^2+x^2y) :xy + 2x(x+1)`

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

`=3x-y-y-x+2x^2+2x`

`=2x^2+4x-2y`

a: \(70a+84b-20ab-24b^2\)

\(=\left(70a+84b\right)-\left(20ab+24b^2\right)\)

\(=14\left(5a+6b\right)-4b\left(5a+6b\right)\)

\(=\left(5a+6b\right)\left(14-4b\right)\)

\(=2\left(7-2b\right)\left(5a+6b\right)\)

b: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2\right)+\left(y^2z+yz^2\right)+3xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+3xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+2xyz+xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2+2yz\right)+yz\left(y+z+x\right)\)

\(=x^2\left(y+z\right)+x\left(y+z\right)^2+yz\left(y+z+x\right)\)

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

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

c: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)

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

\(=x^2\left(y+z\right)+x\left(y^2+z^2+2xz\right)+yz\left(y+z\right)\)

\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y+z\right)^2\)

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

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

a) \(70a+84b-20ab-24b^2\)

\(=\left(70a+84b\right)-\left(20ab+24b^2\right)\)

\(=14\left(5a+6b\right)-4b\left(5a+6b\right)\)

\(=\left(5a+6b\right)\left(14-4b\right)\)

\(=2\left(5a+6b\right)\left(7-2b\right)\)

b) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

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

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

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

c) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)

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

\(=xy\left(x+y\right)+z^2\left(x+y\right)+z\left(x^2+2xy+y^2\right)\)

\(=xy\left(x+y\right)+z^2\left(x+y\right)+z\left(x+y\right)^2\)

\(=\left(x+y\right)\left[xy+z^2+z\left(x+y\right)\right]\)

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

\(=\left(x+y\right)\left[\left(xy+yz\right)+\left(xz+z^2\right)\right]\)

\(=\left(x+y\right)\left[y\left(x+z\right)+z\left(x+z\right)\right]\)

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

a, 70a + 84b - 20ab - 24b²

 = 14.(5a + 6b) - 4b(5a + 6b)

= (5a + 6b).(14 - 4b) 

a, 70a + 84b - 20ab - 24b²

 = (70a + 84b) - (20ab + 24b²)

= 14.(5a + 6b) - 4b.(5a + 6b)

= (5a + 6b).(14 - 4b)