d) \(4x^2y^2-8xy^2+4y^2=4y^2\left(x^2-2x+1\right)=4y^2\left(x-1\right)^2\)

e) \(x^3y+10x^2y+35xy=xy\left(x^2+10x+35\right)\)

f) \(2x^3-4x^2y+2xy^2-8x=2x\left(x^2-2xy+y^2-4\right)=2x\left[\left(x-y\right)^2-4\right]=2x\left(x-y-2\right)\left(x-y+2\right)\)

g) \(3x^2-9xy-6x+18y=3x\left(x-3y\right)-6\left(x-3y\right)=3\left(x-3y\right)\left(x-2\right)\)

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

d: \(4x^2y^2-8xy^2+4y^2\)

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

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

e: \(x^3y+10x^2y+35xy\)

\(=xy\left(x^2+10x+35\right)\)

f: \(2x^3-4x^2y+2xy^2-8x\)

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

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

g: \(3x^2-9xy-6x+18y\)

\(=3x\left(x-3y\right)-6\left(x-3y\right)\)

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

h: \(x^2y^2-3xy^2+2xy-6y\)

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

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

a: \(4x^3-xy^2\)

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

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

b: \(5x^3-10x^2+5x\)

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

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

c: \(4x^2+24x+36-4y^2\)

\(=4\left(x^2+6x+9-y^2\right)\)

\(=4\left(x+3-y\right)\left(x+3+y\right)\)

a) \(4x^3-xy^2=x\left(4x^2-y^2\right)=x\left(2x-y\right)\left(2x+y\right)\)

b) \(5x^3-10x^2+5x=5x\left(x^2-2x+1\right)=5x\left(x-1\right)^2\)

c) \(4x^2+24x+36-4y^2=\left(2x+6\right)^2-4y^2=\left(2x+6-2y\right)\left(2x+6+2y\right)\)

d) \(4x^2y^2-8xy^2+4y^2=4y^2\left(x^2-2x+1\right)=4y^2\left(x-1\right)^2\)

e) \(x^3y+10x^2y+35xy=xy\left(x^2+10x+35\right)\)

f) \(2x^3-4x^2y+2xy^2-8x=2x\left(x^2-2xy+y^2-4\right)=2x\left[\left(x-y\right)^2-4\right]=2x\left(x-y-2\right)\left(x-y+2\right)\)

g) \(3x^2-9xy-6x+18y=3x\left(x-2\right)-9y\left(x-2\right)=3\left(x-2\right)\left(x-3y\right)\)

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

g: \(3x^2-9xy-6x+18y\)

\(=3x\left(x-3y\right)-6\left(x-3y\right)\)

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

h: \(x^2y^2-3xy^2+2xy-6y\)

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

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

a. \(M-P+Q=0\)

\(=>M=P-Q\)

\(=>M=3x^2-2x+5xy^2-7y^2-3xy^2+7y^2+9x^2y+x+5\)

\(=>M=3x^2+2xy^2+9x^2y-x+5\)

b.\(M-P-Q=0\)

\(=>M=P+Q\)

\(=>M=3x^2-2x+5xy^2-7y^2+3xy^2-7y^2-9x^2y-x-5\)

\(=>M=3x^2+8xy^2-14y^2-9x^2y-3x-5\)

a) \(x^3-2x^2-5x+6=0\)

\(\Leftrightarrow\left(x^3-2x^2+x\right)-\left(6x-6\right)=0\\ \Leftrightarrow x\left(x-1\right)^2-6\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left[x\left(x-1\right)-6\right]=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^2-x-6\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-3\right)\left(x+2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x-3=0\\x+2=0\end{matrix}\right.\\ \left[{}\begin{matrix}x=1\\x=3\\x=-2\end{matrix}\right.\)

Vậy ..............................

b) Đặt \(2x^2+7x-3=a\) theo cách đặt ta có :

\(\left(a-5\right)\cdot a=6\)

\(\Leftrightarrow a^2-5a-6=0\)

nhận xét : \(a-b+c=1-\left(-5\right)-6=0\)

\(\Rightarrow a_1=1\)

\(a_2=\dfrac{-6}{1}=-6\)

Với \(a=a_1=1\) \(\Rightarrow2x^2+7x-3=1\)

\(\Leftrightarrow2x^2+7x-4=0\)

\(\Delta=7^2-4\cdot2\cdot\left(-4\right)=49+32=81\) ( \(\sqrt{\Delta}=\sqrt{81}=9\) )

Vì \(\Delta>0\) nên pt có 2 nghiệm phân biệt :

\(x_1=\dfrac{-7+9}{2\cdot2}=\dfrac{1}{2}\)

\(x_2=\dfrac{-7-9}{2\cdot2}=-4\)

Với \(a=a_2=-6\) \(\Rightarrow2x^2+7x-3=-6\\ \Leftrightarrow2x^2+7x+3=0\)

\(\Delta=7^2-4\cdot2\cdot3=49-24=25\)

\(\sqrt{\Delta}=\sqrt{25}=5\)

Vì \(\Delta>0\) nên pt có 2 nghiệm phân biệt :

\(x_3=\dfrac{-7+5}{2\cdot2}=-\dfrac{1}{2}\)

\(x_4=\dfrac{-7-5}{2\cdot2}=-3\)

Vậy \(x_1=\dfrac{1}{2};x_2=-4;x_3=\dfrac{-1}{2};x_4=-3\) là các giá trị cần tìm

M = P + Q

= (3x2y − 2x + 5xy2 − 7y2) + (3xy2 − 7y2 − 9x2y – x – 5)

= 3x2y − 2x + 5xy2 − 7y2 + 3xy2 − 7y2 − 9x2y – x – 5

= (5xy2 + 3xy2) + (3x2y – 9x2y) – (2x + x) – (7y2 + 7y2) – 5

= 8xy2 − 6x2y − 3x − 14y2 – 5.

M = Q – P

= (3xy2 − 7y2 − 9x2y – x – 5) - (3x2y − 2x + 5xy2 − 7y2)

= 3xy2 – 7y2 – 9x2y – x – 5 – 3x2y + 2x – 5xy2 + 7y2.

= (3xy2 – 5xy2) – (9x2y + 3x2y) + (2x – x) + (-7y2 + 7y2) – 5

= -2xy2 − 12x2y + x – 5

a/ 5x²y (x²y– 4xy² + 7xy)

`=5x^4y^2-20x^3y^3+35x^3y^2`

b/ 3xy² (x²y³ + x 2y – xy² )

`=3x^3y^5+3x^3y^3-3x^2y^4`

c/ 3x(12x² + 4x – 5) + 2x(9x² – 6x + 7)

`=36x^3+12x^2-15x+18x^3-18x^2+14x`

`=54x^3-6x^2-x`

d/ 5x(2x² – 9x – 5) – 9x (x² - 7x – 4)

`=10x^3-45x^2-25x-9x^3+63x^2+36x`

`=x^3+18x^2+11x`