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

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

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

a) x³-2x²-x+2

=x(x²-1)+2(-x²+1)

=x(x²-1)-2(x²-1)

=(x²-1)(x-2)

b)

x²+6x-y²+9

=x²+6x+9-y²

=(x+3)²-y²

^{=(x+3-y)(x+3+y)}

a) \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-15\)

\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)-15\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-15\)(1)

Đặt \(x^2+5x+4=t\)

\(\Rightarrow\left(1\right)=t\left(t+2\right)-15=t^2+2t+1-16\)

\(=\left(t+1\right)^2-4^2=\left(t+5\right)\left(t-3\right)\)

\(=\left(x^2+5x+9\right)\left(x^2+5x+1\right)\)

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

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

\(=\left(3x-4\right)\left(x+14\right)\)

a) (x+1)(x+2)(x+3)(x+4) -15

= (x+1)(x+4)(x+2)(x+3)-15

=(x²+5x+4)(x²+5x+6)-15 (*)

đặt x²+5x+5 = k ( k khác 0 )

thì (*) = (k-1)(k+1)-15

=k²-1-15=k²-16

= (k+4)(k-4)

=(x²+5x+9)(x²+5x+1)

b) (2x+5)²-(x-9)²

=(2x+5+x-9)(2x+5-x+9)

=(3x-4)(x+14)

1/\(\left(x^2-25\right)^2-\left(x-5\right)^2\)

<=>\(\left[\left(x-5\right)\left(x+5\right)\right]^2-\left(x-5\right)^2\)

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

2/\(\left(4x^2-25\right)^2-9\left(2x-5\right)^2\)

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

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

 #hoctot<3# 

\(9\left(x-3y\right)^2-25\left(2x+y\right)^2\)

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

\(=\left(3x-9y\right)^2-\left(10x+5y\right)^2\)

\(=\left[3x-9y+10x+5y\right]\left[3x-9y-\left(10x+5y\right)\right]\)

\(=\left(13x-4y\right)\left(-7x-14y\right)\)

\(=-7\left(x+2y\right)\left(13x-4y\right)\)

9(x - 3y)² - 25(2x + y)²

= 3².(x - 3y)² - 5².(2x + y)²

= (3x - 9y)² - (10x + 5y)²

= (3x - 9y - 10x - 5y)(3x - 9y + 10x + 5y)

= (-7x - 14y)(13x - 4y)

= -7(x + 2y)(13x - 4y)

\(x^6+2x^5+x^4-2x^3-2x^2+1=\left(x^3+x^2-1\right)^2\)

a) xy+3x-7y-21

=x(y+3)-7(x+3)

=(x-7)(y+3)

b)2xy-15-6x-5y

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

=(2x-5)(y-3)

c)2x^2y+2xy^2-2x-2y

=2x(xy-1)+2y(xy-1)

=(2x+2y)(xy-1)

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

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

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

Câu cuối mình bị nhầm dòng cuối phải là (x-5)(x+3+x-5)=(x-5)(2x-2)nha bạn

a) xy+3x-7y-21=(xy+3x)-(7y+21)= x(y+3)-7(y+3)=(y+3)(x-7)

b)2xy-15-6x+5y=(2xy-6x)+(5y-15)=2x(y-3)+5(y-3)=(y-3)(2x+5)

c)2x^2y+2xy^2-2x-2y=2xy(x+y)-2(x+y)=2(x+y)(xy-1)

d) x(x+3)-5x(x-5)-5(x+3)=[x(x+3)-5(x+3)]-5x(x-5)=(x+3)(x-5)-5x(x-5)=(x-5)(x+3-5x)=(x-5)(3-4x)

\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)