(x + 2y - 3)²  - 4(x + 2y - 3) + 4

=   (x + 2y - 3)²  - 2. 2. (x + 2y - 3)  +  2²   (hằng đẳng thức số 2, bình phương  của một hiệu)

=  ( x + 2y - 3 - 2)²

= ( x + 2y - 5)²

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

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

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

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

a^3x-x-ab+b

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

=(a-1)(a^2x+xa+x-b)

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

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

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

Đặt \(x^2+3x+1=t\)thay vào (1) ta được :

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

\(=t^2-1+1\)

\(=t^2\)Thay \(t=x^2+3x+1\)ta được:

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

\(=\left(x^2+2.\frac{3}{2}x+\frac{9}{4}-\frac{9}{4}+1\right)^2\)

\(=\left[\left(x+\frac{3}{2}\right)-\frac{5}{4}\right]^2\)

\(=\left(x+\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^2\left(x+\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^2\)

a) 2x.(4x - 1)

câu b), c) mik ko biết

ko mong b cho mik

nhưng vẫn hi vọng b hoặc ai đó sẽ làm vậy
 

b) \(4x^4+1=4x^4+4x^2+1-4x^2\)

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

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

a)  \(8x^2-2x-1=8x^2-4x+2x-1=4x.\left(2x-1\right)+\left(2x-1\right)=\left(2x-1\right)\left(4x+1\right)\)

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

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

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

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

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

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

a, 8x^2-2x-1 = 8x²-4x+2x-1  = 4x ( 2x -1) + (2x-1) = (4x+1)(2x-1) 

b) 4x⁴+1  = (2x²)² + 4x²+ 1 - 4x² = (2x²+1)²-(2x)² = (2x²+1-2x)(2x²+1+2x)

Viết đề rõ chút chứ nhìn ko ra