\(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)

\(=\left(x+1\right)\left(3x^2+3x-5x^2+7\right)\)

\(=\left(x+1\right)\left(-2x^2+3x+7\right)\)

\(x^3+5x^2+5x+1\)

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

\(=\left(x+1\right)\left(x^2+6x+1\right)\)

\(=x^2-5x+\dfrac{25}{4}-\dfrac{29}{4}\)

\(=\left(x-\dfrac{5}{2}\right)^2-\dfrac{29}{4}\)

\(=\left(x-\dfrac{5}{2}-\dfrac{\sqrt{29}}{2}\right)\left(x-\dfrac{5}{2}+\dfrac{\sqrt{29}}{2}\right)\)

\(4x\left(x+1\right)^2-5x^2\left(x+1\right)-4\left(x+1\right) =\left(x+1\right)\left[4x\left(x+1\right)-5x^2-4\right]=\left(x+1\right)\left(4x^2+4x-5x^2-4\right)=\left(x+1\right)\left(-x^2+4x-4\right)=-\left(x+1\right)\left(x-2\right)^2\)

\(4x\left(x+1\right)^2-5x^2\left(x+1\right)-4\left(x+1\right)\)

\(=4x\left(x^2+2x+1\right)-5x^2\left(x+1\right)-4\left(x+1\right)\)

\(=4x^3+8x^2+4x-5x^3-5x-4x-4\)

\(=-x^3+8x^2-5x-4\)

a) x²-x=x(x-1)

b) 3x-3y = 3(x-y)

c)3xy²+6xyz=3xy(y+2z)

d) 5x-20y=5(x-4y)

g) 5x(x-1)-(1-x)=5x(x-1)+(x-1)=(5x+1)(x-1)

a, \(x^2-x=x\left(x-1\right)\)

b, \(3x-3y=3\left(x-y\right)\)

c, \(3xy^2+6xyz=3xy\left(y+2z\right)\)

d, \(5x-20y=5\left(x-4y\right)\)

g, \(5x\left(x-1\right)-\left(1-x\right)=\left(5x+1\right)\left(x-1\right)\)

a,\(x^2-x=x\left(x-1\right)\)

b,\(3x-3y=3\left(x-y\right)\)

c,\(3xy^2+6xyz=3xy\left(y+2z\right)\)

d,\(5x-20y=5\left(x-4y\right)\)

g,\(5x\left(x-1\right)-\left(1-x\right)=5x\left(x-1\right)+\left(x-1\right)=\left(x-1\right)\left(5x+1\right)\)

-Đặt \(t=\left(x^2-x+1\right)\)

\(\left(x^2-x+1\right)^2-5x\left(x^2-x+1\right)+4x^2\)

\(=t^2-5xt+4x^2\)

\(=t^2-4xt-xt+4x^2\)

\(=t\left(t-4x\right)-x\left(t-4x\right)\)

\(=\left(t-4x\right)\left(t-x\right)\)

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

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

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

a) \(x^2-xy+x-y\)

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

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

b) \(x^2+5x+6\)

\(=x^2+2x+3x+6\)

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

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

\(2xy-x^2-y^2+16\)

\(=16-\left(x-y\right)^2\)

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

`#3107.101107`

a)

`A = 2x^2 + 5x^3 + x^2y`

`= x^2 * (2 + 5x + y)`

b)

`5x(x - 1) + 15(x - 1)`

`= (5x + 15)(x - 1)`

`= 5(x + 3)(x - 1)`

\(a)A=2x^2+5x^3+x^2y\\=x^2(2+5x+y)\\=x^2(5x+y+2)\\---\\b)5x(x-1)+15(x-1)\\=(5x+15)(x-1)\\=5(x+3)(x-1)\)

\(Toru\)