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

b: \(=3\left[\left(x+y\right)^2-2xy\right]-2\left[\left(x-y\right)^3+3xy\left(x-y\right)\right]\)

\(=3\left(1-2xy\right)-2\left(1+3xy\right)\)

\(=3-6xy-2-6xy=-12xy+1\)

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

\(=101^2-3\cdot101^2+3\cdot101+2012\)

=1002013

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

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

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

đề bài là gì, phân tích đa thức hay tính

phân tích đa thức thành nhân tử à bạn :)))

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

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

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

\(E=\left(x^3+3xy^2+3x^2y+y^3\right)+3\left(x+y\right)-3\left(x^2+2xy+y^2\right)+2016\)

\(=\left(x+y\right)^3+3\left(x+y\right)-3\left(x+y\right)^2+2016\)

\(=21^3+3.21-3.21^2+2016\)

\(=\left(21-1\right)^3+2017=8000+2017=10017\)

Mình không viết lại đề nha ~

\(E=\left(x^3+3xy^2+3x^2y+y^3\right)+\left(3y+3x\right)+\left(3x^2+6xy+3y^2\right)+2016\)

\(E=\left(x+y\right)^3+3\left(x+y\right)+3\left(x+y\right)^2+2016\)

\(E=\left(x+y\right)[\left(x+y\right)^2+3+\left(x+y\right)]+2016\)

\(E=21\left(21^2+3+21\right)+2016\)

\(E=21.465+2016\)

\(E=9765+2016=11781\)

a) 5x - 5y + ax - ay = 5(x - y) + a(x - y)

= (5 + a)(x - y)

b) x³ - x + 3x²y + 3xy² + y³ - y

= (x³ + 3x²y + 3xy² + y³) - (x + y)

= (x + y)³ - (x + y)

= (x + y)[(x + y)² - 1]

= (x + y)(x + y + 1)(x + y - 1)

c) x² - 2x - 3 = x² + x - 3x -3

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

= (x - 3)(x + 1)

e) 6x - 9 - x² = 3x - 9 + 3x - x²

= 3(x - 3) + x(3 - x)

= 3(x - 3) - x(x - 3)

= (3 - x)(x - 3)