\(x^2+2xy+y^2+2x+2y-15\)

\(=\left(x+y\right)^2+2\left(x+y\right)+1-16\)

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

\(x^2+2xy+y^2+2x+2y-15\)

\(=x^2+2xy+y^2+2x+2y+1-16\)

\(=\left(x+y\right)^2+2\left(x+y\right)+1-16\)

Đặt \(x+y=t\)

\(\Rightarrow t^2+2t+1-16\)

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

\(=\left(t+1-4\right)\left(t+1+4\right)\)

\(=\left(t-3\right)\left(t+5\right)\)

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

phân tích đa thức thành nhân tử 4x^3+6x^2+4x+1

= 4x^3+6x^2+4x+1

= (2x+1)(2x^2+2x+1)

nha bạn chúc bạn học tốt nha 

\(4x^3+6x^2+4x+1\)

\(=4x^3+4x^2+2x^2+2x+2x+1\)

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

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

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

phân tích đa thức thành nhân tử 6x^3+x^2+x+1

= 6x^3+x^2+x+1

= (2x+1)(3x^2-x+1)

chúc bạn học tốt nha 

6x³ + x² + x+1

=6x³ +3x² - 2x² - x + 2x +1

= 3x²(2x + 1) - x(2x + 1) + (2x+1)

=(2x+1)(3x² -x +1) 

\(x^3+3x^2-10x-24\)

\(=x^3-3x^2+6x^2-18x+8x-24\)

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

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

\(=\left(x-3\right)\left(x^2+6x+9-1\right)\)

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

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

\(2x^3-11x^2+10x+8\)

\(=2x^3-4x^2-7x^2+14x-4x+8\)

\(=2x^2\left(x-2\right)-7x\left(x-2\right)-4\left(x-2\right)\)

\(=\left(x-2\right)\left(2x^2-7x-4\right)\)

\(=\left(x-2\right)[2x\left(x-4\right)+\left(x-4\right)]\)

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

Ta có: \(^{3x^3-4x^2+13x-4}\) = \(3x^3-x^2-3x^2+x+12x-4\)

                                       = \(3x^2\left(x-\frac{1}{3}\right)-3x\left(x-\frac{1}{3}\right)+12\left(x-\frac{1}{3}\right)\)

                                       = \(\left(3x^2-3x+12\right)\left(x-\frac{1}{3}\right)\)

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

 3x^3-4x^2+13x-4

= (3x-1)(x^2-x+4)

nha bạn 

\(2x^3-35x+75=2x^3+10x^2-10x^2-50x+15x+75\)

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

Trả lời:

Sửa đề: \(2x^2-35x+75\)

\(=2x^2-30x-5x+75\)

\(=\left(2x^2-30x\right)-\left(5x-75\right)\)

\(=2x\left(x-15\right)-5\left(x-15\right)\)

\(=\left(x-15\right)\left(2x-5\right)\)

a. Đặt \(x^2-2y=a\)

ta có : \(\left(x^2-2y\right)^2-4\left(x^2-2y\right)-12=a^2-4a-12=a^2-6a+2a-12=\left(a-6\right)\left(a+2\right)\)

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

b. Đặt \(x+6=a\Rightarrow\left(x+3\right)\left(x+6\right)\left(x+9\right)+45=\left(a-3\right)a\left(a+3\right)+45\)

\(=a^3-9a+45\) nghiệm xấu quá không nhóm được ban ơi :((