Ta có:

\(x^9-x^7-x^6-x^5+x^4+x^3+x^2-1\)

\(=\left(x^9-x^8\right)+\left(x^8-x^7\right)-\left(x^6-x^5\right)-\left(2x^5-2x^4\right)-\left(x^4-x^3\right)+\left(x^2-x\right)+\left(x-1\right) \)

\(=x^8.\left(x-1\right)+x^7.\left(x-1\right)-x^5.\left(x-1\right)-2x^4.\left(x-1\right)-x^3\left(x-1\right)+x\left(x-1\right)+\left(x-1\right)\)

\(=\left(x-1\right)\left(x^8+x^7-x^5-2x^4-x^3+x+1\right)\)

xin chào làm ơn đừng trách mk mk sẽ nói cách giải

h: Ta có: \(x\left(x+2\right)\left(x+4\right)\left(x+6\right)+15\)

\(=\left(x^2+6x\right)\left(x^2+6x+8\right)+15\)

\(=\left(x^2+6x\right)^2+8\left(x^2+6x\right)+15\)

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

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

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

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

=x(7x+3)(x-1)

2: \(9\left(x+5\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15\right)^2-\left(x-7\right)^2\)

=(3x+15+x-7)(3x+15-x+7)

=(4x+8)(2x+22)

\(=4\left(x+2\right)\cdot2\cdot\left(x+11\right)=8\left(x+2\right)\left(x+11\right)\)

3: \(x^2-2xy+y^2-xz+yz\)

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

=(x-y)(x-y-z)

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

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

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

5: \(9x^2y^2+15x^2y-21xy^2\)

\(=3xy\cdot3xy+3xy\cdot5x-3xy\cdot7y\)

=3xy(3xy+5x-7y)

6: \(x^3-2x^2y+xy^2-9xy^4\)

\(=x\left(x^2-2xy+y^2-9y^4\right)\)

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

7: \(x^2+x-12\)

\(=x^2+4x-3x-12\)

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

=(x+4)(x-3)

8: (x+1)(x+3)(x+5)(x+7)+15

\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)

\(=\left(x^2+8x+7\right)^2+8\left(x^2+8x+7\right)+15\)

\(=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)

\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)

a/\(\left(x^2-x\right)^2+4\left(x^2-x\right)-12.\)

cho \(\left(x^2-x\right)=a\)

\(\Rightarrow a^2+4a-12\)

\(=a^2+6a-2a-12\)

\(=\left(a^2+6a\right)-\left(2a+12\right)\)

\(=a\left(a+6\right)-2\left(a+6\right)\)

\(=\left(a+6\right)\left(a-2\right)\)

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

b/ \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)-24\)

\(=\left(x^2+4x+x+4\right)\left(x^2+3x+2x+6\right)-24\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

Gọi \(x^2+5x+5=a\)

\(\Rightarrow\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24=\left(a-1\right)\left(a+1\right)-24\)

                                                                                 \(=a^2-1-24\)

                                                                                \(=a^2-25\)

                                                                                \(=\left(a-5\right)\left(a+5\right)\)

                                                                               \(\Rightarrow\left(x^2+5x+5-5\right)\left(x^2+5x+5+5\right)\)

                                                                                \(=\left(x^2+5x\right)\left(x^2+5x+10\right)\)

\(\Rightarrow\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)\(=\left(x^2+5x\right)\left(x^2+5x+10\right)\)

a) \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-15\left(1\right)=\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]-15=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-15\)

Đặt \(t=x^2+5x+4\)

(1) trở thành: \(t\left(t+2\right)-15=t^2+2t+1-16=\left(t+1\right)^2-4^2=\left(t-3\right)\left(t+5\right)\)

Thay t: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-15=\left(x^2+5x+4-3\right)\left(x^2+5x+4+5\right)=\left(x^2+5x+1\right)\left(x^2+5x+9\right)\)

b) \(\left(2x+5\right)^2-\left(x-9\right)^2=\left(2x+5-x+9\right)\left(2x+5+x-9\right)=\left(x+14\right)\left(3x-4\right)\)

a: Ta có: \(\left(x+1\right)\cdot\left(x+2\right)\left(x+3\right)\left(x+4\right)-15\)

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

\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24-15\)

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

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

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

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

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