(x - 4)(x² + 4x + 16) - x(x² - 6) = 2

x³ - 64 - x³ + 6x = 2

6x = 2 + 64

6x = 66

x = 66 : 6

x = 11

x³ - 27 + 3x(x - 3)

= (x - 3)(x² + 3x + 9) + 3x(x - 3)

= (x - 3)(x² + 3x + 9 + 3x)

= (x - 3)(x² + 6x + 9)

= (x - 3)(x + 3)²

5x³ - 7x² + 10x - 14

= 5x(x² + 2) - 7(x² + 2)

= (x² + 2)(5x - 7)

a) 20x³y² - 25x²y³ + 5x²y²

= 5x²y²(4x - 5y + 5) 

b) Ta có x³ - 25x = 0

<=> x(x² - 25) = 0

<=> x(x - 5)(x + 5) = 0

<=> x = 0 hoặc x - 5 = 0 hoặc x + 5 = 0

<=> x = 0 hoặc x = 5 hoặc x = -5

Vậy x \(\in\left\{0;5;-5\right\}\)là nghiệm phương trình

c) (x + 3)² = x + 3

<=> (x + 3)² - (x + 3) = 0

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

<=> (x + 3)(x + 2) = 0

<=> \(\orbr{\begin{cases}x+3=0\\x+2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-3\\x=-2\end{cases}}\)

Vậy x \(\in\left\{-3;-2\right\}\)

a) \(x^2-xy+x-y\)

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

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

b) \(x^2+5x+6\)

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

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

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

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

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

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

ta có :

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

\(=\left(x-y\right)\left(x+y-5\right)\)

x²-5x+5y-y²

=(x²-y²)-(5x-5y)

=(x-y)(x+y)-5(x-y)

=(x-y)(x+y-5)

\(x^2-4x+3=x^2-3x-x+3=x\left(x-3\right)-\left(x-3\right)=\left(x-1\right)\left(x-3\right)\)

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

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

\(x^4+4=\left(x^2\right)^2+2.x^2.2+2^2-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2+2\right)^2-\left(2x^2\right)=\left(x^2+2+2x\right)\left(x^2-2-2x\right)\)

Nhần mình ấn lộn bài sory m.n

Ta có : 5x³ - 45x

= 5x(x² - 9)

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

b ) Ta có : 3x² - 7x - 6 

= 3x² - 9x + 2x - 6 

= 3x (x - 3) + 2(x - 3)

= (x - 3)(3x + 2)

\(a,=\left(x+y\right)\left(x+3\right)\\ b,=\left(x+2\right)\left(x+3\right)\)

e) \(8\left(x+3y\right)-16x\left(x+3y\right)=\left(x+3y\right)\left(8-16x\right)=8\left(x+3y\right)\left(1-2x\right)\)

f) \(4x^2\left(x+1\right)+2x^2\left(x+1\right)=\left(x+1\right)\left(4x^2+2x^2\right)=6x^2\left(x+1\right)\)

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

mn ơiiiiiiiiiiiii