b. \(N=x^3-3x^2+3x^2y+3xy^2+y^3-3y^2-6xy+3x+3y+2012\)\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(3x^2+6xy+3y^2\right)+\left(3x+3y\right)+2012\)

\(=\left(x+y\right)^3-3\left(x^2+2xy+y^2\right)+3\left(x+y\right)+2012\)

\(=\left(x+y\right)^3-3\left(x+y\right)^2+3\left(x+y\right)+2012\) (*)

Thay x + y =101 vào biểu thức (*) ta được:

\(N=101^3-3.101^2+3.101+2012\)

= 1002013

Câu a ko hỉu đề!

Câu b:

Ta có: N = \(x^3-3x^2+3x^2y+3xy^2+y^3-3y^2-6xy+3x+3y+2012\)

= \(\left(x^3+3x^2y+3xy^2+y^3\right)-3\left(x^2+2xy+y^2\right)+3\left(x+y\right)+2012\)

= \(\left(x+y\right)^3-3\left(x+y\right)^2+3\left(x+y\right)+2012\)

= \(\left(x+y-1\right)^3+2013\)

Thay x + y = 101 vào N ta được:

N = 100³ + 2013 = 1002013

B= x²(y-z)+y²(z-x)+z²(x-y)

= x²(y-z)+y²z-xy²+xz²-yz²

= x²(y-z)+yz(y-z)-x(y²-z²)

= x²(y-z)+yz(y-z)-x(y-z)(y+z)

= (y-z)(x²+yz -xy -xz)

= (y-z)[x(x-y)-z(x-y)]

= (y-z)(x-y)(x-z)

Bài 2:

1: \(\left(2x-1\right)^2-4\left(2x-1\right)=0\)

=>\(\left(2x-1\right)\left(2x-1-4\right)=0\)

=>(2x-1)(2x-5)=0

=>\(\left[{}\begin{matrix}2x-1=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)

2: \(9x^3-x=0\)

=>\(x\left(9x^2-1\right)=0\)

=>x(3x-1)(3x+1)=0

=>\(\left[{}\begin{matrix}x=0\\3x-1=0\\3x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\\x=-\dfrac{1}{3}\end{matrix}\right.\)

3: \(\left(3-2x\right)^2-2\left(2x-3\right)=0\)

=>\(\left(2x-3\right)^2-2\left(2x-3\right)=0\)

=>(2x-3)(2x-3-2)=0

=>(2x-3)(2x-5)=0

=>\(\left[{}\begin{matrix}2x-3=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)

4: \(\left(2x-5\right)\left(x+5\right)-10x+25=0\)

=>\(2x^2+10x-5x-25-10x+25=0\)

=>\(2x^2-5x=0\)

=>\(x\left(2x-5\right)=0\)

=>\(\left[{}\begin{matrix}x=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{5}{2}\end{matrix}\right.\)

Bài 1:

1: \(3x^3y^2-6xy\)

\(=3xy\cdot x^2y-3xy\cdot2\)

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

2: \(\left(x-2y\right)\left(x+3y\right)-2\left(x-2y\right)\)

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

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

3: \(\left(3x-1\right)\left(x-2y\right)-5x\left(2y-x\right)\)

\(=\left(3x-1\right)\left(x-2y\right)+5x\left(x-2y\right)\)

\(=(x-2y)(3x-1+5x)\)

\(=\left(x-2y\right)\left(8x-1\right)\)

4: \(x^2-y^2-6y-9\)

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

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

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

5: \(\left(3x-y\right)^2-4y^2\)

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

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

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

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

6: \(4x^2-9y^2-4x+1\)

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

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

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

8: \(x^2y-xy^2-2x+2y\)

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

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

9: \(x^2-y^2-2x+2y\)

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

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

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

P = 3x² - 2x + 3y² - 2y + 6xy - 100

= (3x² + 6xy + 3y²) - (2x + 2y) - 100

= 3(x² + 2xy + y²) - 2(x + y) - 100

= 3(x + y)² - 2.5 - 100

= 3. 5² -10 - 100

= 75 - 10 - 100 = -35

Q = x³ + y³ - 2x² - 2y² + 3xy(x + y) - 4xy + 3(x+y) +10

= x³ + y³ - 2x² - 2y² + 3x²y + 3xy² - 4xy + 3.5 + 10

= (x³ + 3x²y + 3xy² + y³) - (2x² + 4xy + 2y²) + 15 + 10

= (x + y)³ - 2(x² + 2xy + y²) + 25

= 5³ - 2(x + y)² +25

= 125 - 2. 5² + 25

= 125 - 50 + 25 = 100

\(B=x^3+3x^2+3x^2y+3xy^2+y^3+3y^2+6xy+3x+3y+2019\)

\(=\left(x+y\right)^3-3\left(x+y\right)^2+3\left(x+y\right)+2019\)

\(=\left[\left(x+y\right)^3-3\left(x+y\right)^2+3\left(x+y\right)+1\right]+2018\)

\(=\left(x+y-1\right)^3+2018\)

Mà \(x+y=101\)

\(B=\left(101-1\right)^3+2018=1002018\)

P = 3x² - 2x + 3y² - 2y + 6xy +2018

P = 3(x² + y² + 2xy) - 2(x + y) + 2018

P = 3[(x + y)² - 2xy + 2xy] -2.5 + 2018

P = 3[ 5² +0] - 10 + 2018

P = 3.25 + 2008

P = 75 + 2008

P = 2083