Đặt \(x^2+3x+1=t\)

\(\Rightarrow\left(x^2+3x+1\right)\left(x^2+3x+2\right)-6=t.\left(t+1\right)-6\)

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

\(=t\left(t-2\right)+3\left(t-2\right)=\left(t-2\right)\left(t+3\right)\)

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

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

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

Đặt \(x^2+3x+1=a\)ta có :

\(a\left(a+1\right)-6\)

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

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

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

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

\(=\left(a+6\right)\left(a-1\right)\)

Thay \(a=x^2+3x+1\)vào A ta có :

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

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

a: \(x^4+x^2+2x+6\)

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

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

bạn hãy dùng máy tính tìm nghiệm là đc bạn nhé ! như vậy sẽ nhanh hơn ! 

a, 2x² + 10xy=2x(x+5y)
b, 3x ( y - x ) + 6y ( y - x )=(3x+6y)(y-x)
c, 3x ( x - 2 ) - x + 2 + 5x ( x - 2 )=3x(x-2)-(x-2)+5x(x-2)=(8x-1)(x-2)

giúp mik vs các bạn

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

a)3x^2-7x+2

=3x^2-x-6x+2

=(3x^2-x)-(6x-2)

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

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

cho loi nx nha may ban

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

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

\(=x^2+6x+9-\left(2x-6x^2+6-18x\right)+9x^2+6x+1\)

\(=10x^2+12x+10+6x^2+16x-6=16x^2+28x+4\)

\(=4\left(4x^2+7x+1\right)\)

a, 3x(x^2-4)=0

+3x=0=>x=0

+x^2-4=0

=>x^2=4

=>x=+-2

c,x(x+2)-3x-6=0

x(x+2)-3(x+2)=0

(x+2)(x-3)=0

TH1 :x+2=0

x=-2

TH2 : x-3=0

x=3

câu b bạn chờ mình chúc nha

nhớ k cho mình