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

\(x^2-9-\left(x-3\right)\left(5-2x\right)=\left(x-3\right)\left(x+3\right)-\left(x-3\right)\left(5-2x\right)=\left(x-3\right)\left(x+3-5+2x\right)=\left(x-3\right)\left(3x-2\right)\)

\(x^2-9-\left(x-3\right)\left(5-2x\right)\\ =\left(x^2-9\right)-\left(x-3\right)\left(5-2x\right)\\ =\left(x-3\right)\left(x+3\right)-\left(x-3\right)\left(5-2x\right)\\ =\left(x-3\right)\left(x+3-5+2x\right)\\ =\left(x-3\right)\left(3x-2\right)\)

Ta có x(x+3)(x+2)(x+5)+9= x(x+5).(x+2)(x+3) +9= (x²+5x)(x²+5x+6)+9

Đặt x²+5x+3=a ta được

(a-3).(a+3)+9= a²-9+9=a²

Thay x²+5x+3 vào biểu thức trên ta được

(x²+5x+3)²

Vậy x(x+3)(x+2)(x+5)= (x²+5x+3)²

\(x\left(x+3\right)\left(x+2\right)\left(x+5\right)+9\)

\(=\left(x^2+5x\right)\left(x^2+5x+6\right)+9\)

\(=\left[\left(x^2+5x+3\right)-3\right]\left[\left(x^2+5x+3\right)+3\right]+9\)

\(=\left(x^2+5x+3\right)^2-9+9\)

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

bạn pham trung thanh 

kết quả phải là (x²+5x+3)²

M = x⁹ - x⁷ + x⁶ - x⁵ - x⁴ + x³ - x² + 1

= ( x⁹ - x⁷ ) + ( x⁶ - x⁴ ) - ( x⁵ - x³ ) - ( x² - 1 )

= x⁷( x² - 1 ) + x⁴( x² - 1 ) - x³( x² - 1 ) - ( x² - 1 )

= ( x² - 1 )( x⁷ + x⁴ - x³ - 1 )

= ( x - 1 )( x + 1 )[ x⁴( x³ + 1 ) - ( x³ + 1 ) ]

= ( x - 1 )( x + 1 )( x³ + 1 )( x⁴ - 1 )

= ( x - 1 )( x + 1 )( x + 1 )( x² - x + 1 )( x² - 1 )( x² + 1 )

= ( x + 1 )²( x - 1 )( x² - x + 1 )( x - 1 )( x + 1 )( x² + 1 )

= ( x + 1 )³( x - 1 )²( x² + 1 )( x² - x + 1 )

\(x-\sqrt{x}-6=\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)\)

\(2x+5\sqrt{x}-3=\left(\sqrt{x}+3\right)\left(2\sqrt{x}-1\right)\)

\(1,\\ 1,=15\left(x+y\right)\\ 2,=4\left(2x-3y\right)\\ 3,=x\left(y-1\right)\\ 4,=2x\left(2x-3\right)\\ 2,\\ 1,=\left(x+y\right)\left(2-5a\right)\\ 2,=\left(x-5\right)\left(a^2-3\right)\\ 3,=\left(a-b\right)\left(4x+6xy\right)=2x\left(2+3y\right)\left(a-b\right)\\ 4,=\left(x-1\right)\left(3x+5\right)\\ 3,\\ A=13\left(87+12+1\right)=13\cdot100=1300\\ B=\left(x-3\right)\left(2x+y\right)=\left(13-3\right)\left(26+4\right)=10\cdot30=300\\ 4,\\ 1,\Rightarrow\left(x-5\right)\left(x-2\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ 2,\Rightarrow\left(x-7\right)\left(x+2\right)=0\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ 3,\Rightarrow\left(3x-1\right)\left(x-4\right)=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=4\end{matrix}\right.\\ 4,\Rightarrow\left(2x+3\right)\left(2x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)

x⁹+x³+x²+x¹

= (x⁹-x⁶)+(x⁶-x³)+x²+x+1

= x⁶(x³-1)+x³(x³-1)+x²+x+1

= x⁶(x-1)(x²+x+1)+x³(x-1)(x²+x+1)+(x²+x+1)

= (x²+x+1)(x⁷-x⁶+x⁴-x³+1)