a) Ta có: \(x-2y+x^2-4y^2\)

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

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

b) Ta có: \(x^2+2xy+y^2-4x^2y^2\)

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

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

c) Ta có: \(x^6-x^4+2x^3+2x^2\)

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

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

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

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

d) Ta có: \(x^3+3x^2+3x+1-8y^3\)

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

\(=\left(x+1-2y\right)\left[\left(x+1\right)^2+2y\left(x+1\right)+4y^2\right]\)

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

a, \(x-2y+x^2-4y^2=\left(x-2y\right)+\left(x-2y\right)\left(x+2y\right)=\left(x-2y\right)\left(1+x+2y\right)\)

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

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

c, \(x^6-x^4+2x^3+2x^2=x^6+2x^3+1-x^4+2x^2-1\)

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

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

d, \(x^3+3x^2+3x+1-8y^3=\left(x+1\right)^3-\left(2y\right)^3=\left(x+1-2y\right)\left(x+1+2y\right)\)

a) Ta có: \(x-2y+x^2-4y^2\)

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

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

b: Ta có: \(x^2-4x^2y^2+y^2+2xy\)

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

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

a) \(x^2 (x+1)-2x(x+1)+x+1 \\ =(x+1)(x^2-2x+1)\\=(x+1)(x-1)^2\)

b) \(4x^2 -8x+3 \\= (2x^2)-2.2x .2 + 2^2 -1 \\=(2x-2)^2-1^2\\=(2x-2+1)(2x-2-1)\\= (2x-1)(2x-3)\)

a)  \(A=\left(x+2\right)\left(x+3\right)\left(x+5\right)\left(x+6\right)-10\)

\(=\left(x^2+8x+12\right)\left(x^2+8x+15\right)-10\)

Đặt   \(x^2+8x+12=t\)

Khi đó ta có: 

\(A=t\left(t+3\right)-10\)

   \(=t^2+3t-10\)

   \(=\left(t-2\right)\left(t+5\right)\)

Thay trở lại ta có:

\(A=\left(x^2+8x+10\right)\left(x^2+8x+17\right)\)

b)  \(B=x\left(2x+1\right)\left(2x+3\right)\left(4x+8\right)-18\)

\(=\left(4x^2+8x\right)\left(4x^2+8x+3\right)-18\)

Đặt  \(4x^2+8x=t\)

Khi đó ta có:

\(B=t\left(t+3\right)-18=t^2+3t-18=\left(t-3\right)\left(t+6\right)\)

Thay trở lại ta có:

\(B=\left(4x^2+8x-3\right)\left(4x^2+8x+6\right)=2\left(4x^2+8x-3\right)\left(2x^2+4x+3\right)\)

a: =(x^2+x)^2+3(x^2+x)-10

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

=(x^2+x+5)(x+2)(x-1)

b: (x^2+2x)^2-2(x^2+2x)-3

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

=(x+1)^2*(x+3)(x-1)

c: =(x^2+x)^2+4(x^2+x)-12

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

=(x^2+x+6)(x+2)(x-1)

d: =(x^2+10x+16)(x^2+10x+24)+16

=(x^2+10x)^2+40(x^2+10x)+400

=(x^2+10x+20)^2

giúp mik gấp vs ạ đag cần trong đêm nay

\(\left(x+1\right)\left(x+3\right)\left(x+4\right)\left(x+6\right)-7\)

\(=\left\{\left(x+1\right)\left(x+6\right)\right\}.\left\{\left(x+3\right)\left(x+4\right)\right\}-7\)

\(=\left(x^2+7x+6\right)\left(x^2+7x+12\right)-7\) \(\left(1\right)\)

đặt \(x^2+7x+9=a\)

<=> \(\left(1\right)=\left(a-3\right)\left(a+3\right)-7\)

             \(=a^2-16\)

               \(=\left(a-4\right)\left(a+4\right)\)

hay\(\left(1\right)=\) \(\left(x^2+7x+9-4\right)\left(x^2+7x+9+4\right)\)

               \(=\left(x^2+7x+5\right)\left(x^2+7x+13\right)\)

những câu còn lại cũng nhóm đầu với cuối , hai cái giữa với nhau , xong làm tương tự câu trên

học tốt

a) (x + 1)(x + 3)(x + 4)(x + 6) - 7

= (x + 1)(x + 6) (x + 3)(x + 4) - 7

= (x² + 7x + 6)(x + 7x + 12) - 7

Đặt t = x² + 7x + 6

Ta có : t(t + 6) - 7 

= t² + 6t - 7

= t² + 6t + 9 - 16 

= (t + 3) - 16

= (t + 3 - 4)(t + 3 + 4)

= (t - 1)(t + 7)

Nên : 

Pt = (x² + 7x + 6 - 1)(x² + 7x + 6 + 7)

=   (x² + 7x + 5)(x² + 7x + 13)

Phân tích đa thức thành nhân tử:

a) (x+1)(x+3)(x+4)(x+6)-7

b)(x+2)(x+3)(x+5)(x+6)-10

c) x(2x+1)(2x+3)(4x+8)-18

Làm : 

a) (x + 1)(x + 3)(x + 4)(x + 6) - 7

= (x + 1)(x + 6) (x + 3)(x + 4) - 7

= (x² + 7x + 6)(x + 7x + 12) - 7

Đặt t = x² + 7x + 6

Ta có : t(t + 6) - 7 

= t² + 6t - 7

= t² + 6t + 9 - 16 

= (t + 3) - 16

= (t + 3 - 4)(t + 3 + 4)

= (t - 1)(t + 7)

Nên : 

Pt = (x² + 7x + 6 - 1)(x² + 7x + 6 + 7)

=   (x² + 7x + 5)(x² + 7x + 13)

a,     \(x\left(x-1\right)\left(x-2\right)\left(x-3\right)-3\)

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

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

Đặt \(x^2-3x=t\Rightarrow x^2-3x+2=t+2\) Ta có: 

      \(x\left(x-1\right)\left(x-2\right)\left(x-3\right)-3\)

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

\(=t^2+2t-3\)

\(=t^2+3t-t-3\)

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

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

Các ý khác cũng tương tự nhóm số đầu với số cuối và nhóm 2 số còn lại rồi đặt biến phụ.

b, \(\left(x^2+7x+5\right)\left(x^2+7x+13\right)\)

c, \(\left(x^2+8x+10\right)\left(x^2+8x+17\right)\)

d, \(\left(4x^2+8x-3\right)\left(4x^2+8x+6\right)\)

Chúc bạn học tốt.

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

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

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