\(=2\left(x^2-y^2\right)-6\left(x+y\right)=2\left(x-y\right)\left(x+y\right)-6\left(x+y\right)=\left(x+y\right)\left(2x-2y-6\right)\)                                                                                    Đảm bảo chuẩn ko cần chỉnh (•••

  check mk nhá
 

2X²-2Y²-6X-6Y

=2(X²-Y²) +6(X-Y)

=2(X-Y)(X+Y)+3.2(X-Y)

=2(X-Y)(X+Y+3X-3Y)

=2(X-Y)(4X-2Y)

=4(X-Y)(2X-Y)

\(2x^2-2y^2-6x-6y\)

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

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

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

\(4\left(x+3y-4\right)^2-x^2+6x-9\)

\(=\left[2\left(x+3y-4\right)\right]^2-\left(x^2-6x+9\right)\)

\(=\left[2x+6y-8\right]^2-\left(x-3\right)^2\)

\(=\left(2x+6y-8+x-3\right)\left(2x+6y-8-x+3\right)\)

\(=\left(3x+6y-11\right)\left(x+6y-5\right)\)

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

\(=x^4+16x^2+9+8x^3-24x-6x^2-5x^2-20x+15+6x^2\)

\(=x^4+8x^3+11x^2-44x+24\)

\(=\left(x^4-x^3\right)+\left(9x^3-9x^2\right)+\left(20x^2-20x\right)-\left(24x-24\right)\)

\(=x^3\left(x-1\right)+9x^2\left(x-1\right)+20x\left(x-1\right)-24\left(x-1\right)\)

\(=\left(x-1\right)\left(x^3+9x^2+20x-24\right)\)

x²-y²+6x+6y = (x²-y²)+(6x+6y) = (x-y)(x+y)+6(x+y) = (x-y-6)(x+y)

\(a,\)\(x^3-13x-12\)

\(=x^3-x-12x-12\)

\(=x\left(x^2-1\right)-12\left(x+1\right)\)

\(=x\left(x-1\right)\left(x+1\right)-12\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x-12\right)\)

\(=\left(x+1\right)\left(x^2-4x+3x-12\right)\)

\(=\left(x+1\right)\left[x\left(x-4\right)+3\left(x+4\right)\right]\)

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

a) \(x^3-13x-12\)

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

\(=x^2\left(x+1\right)-x\left(x+1\right)-12\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-x-12\right)\)

\(=\left(x+1\right)\left(x^2-4x+3x-12\right)\)

\(=\left(x+1\right)\left[x\left(x-4\right)+3\left(x-4\right)\right]\)

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

b) \(2x^4+3x^3-9x^2-3x+2\)câu này hình như sai đề rồi, bạn xem lại nhen

c) \(x^4-3x^3-6x^2+3x+1\)câu này cx thế, bạn xem lại nha

b) \(2x^4+3x^3-9x^2-3x+2\)

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

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

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

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

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

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

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

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

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

\(=x\left[x^2\left(x-y\right)^2-36y^2\right]\\ =x\left[x\left(x-y\right)-6y\right]\left[x\left(x-y\right)+6y\right]\\ =x\left(x^2-xy-6y\right)\left(x^2-xy+6y\right)\)

bài 2 là tìm X nha mn

\(1,\\ a,=x\left(2x+3y-5\right)\\ b,=x\left(x-2y\right)+\left(x-2y\right)=\left(x+1\right)\left(x-2y\right)\\ 2,\\ a,\Leftrightarrow x\left(x+4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-4\end{matrix}\right.\\ b,\Leftrightarrow x\left(x-2y\right)+\left(x-2y\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x-2y\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2y\left(y\in R\right)\end{matrix}\right.\)