1: =(16x^2-8x+1)-y^2

=(4x-1)^2-y^2

=(4x-1-y)(4x-1+y)

2: =(x^2-2xy+y^2)-z^2

=(x-y)^2-z^2

=(x-y-z)(x-y+z)

3: =(x^2+4xy+4y^2)-16

=(x+2y)^2-4^2

=(x+2y-4)(x+2y+4)

4: =(x^2-4xy+4y^2)-16

=(x-2y)^2-4^2

=(x-2y-4)(x-2y+4)

\(x^2+y^2-4xy-1\) 

⇔\(\left(x-y\right)^2-1\) 

⇔\(\left(x-y+1\right)\left(x-y-1\right)\)

a) 25 - x2 + 4xy - 4y2 = 25 - (x2  - 4xy + 4y2 ) = 52  - (x - 2y)2  = (5 + x - 2y)(5 - x +2y) = (x - 2y + 5)(2y - x + 5)

Chú ý x2 là \(x^2\)mk ko tiện nên ko ghi mong bn thông cảm

nếu thấy đúng nhé@@

-1 nữa bạn ơi

\(4x^2-4xy+y^2\)

\(=\left(2x\right)^2-2\cdot2x\cdot y+y^2\)

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

\(---\)

\(\left(x+1\right)^2-9y^2\)

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

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

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

\(---\)

\(2x+5^2-9x^2\) (kt lại đề bài)

\(2x-1^2-3x-1^2\)

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

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

b) \(\left(1+x^2\right)\left(1+y^2\right)+4xy+2\left(x+y\right)\left(1+xy\right)=25\Leftrightarrow1+x^2+y^2+x^2y^2+4xy+2\left(x+y\right)\left(1+xy\right)-25=0\Leftrightarrow\left(x+y\right)^2+2\left(x+y\right)\left(1+xy\right)+\left(1+xy\right)^2-25=0\Leftrightarrow\left(x+y+1+xy\right)^2-25=0\Leftrightarrow\left(x+y+xy-24\right)\left(x+y+xy+26\right)=0\)

a: Ta có: \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

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

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

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

bạn viết lại đề đi, có số mũ, xuống dòng chứ thế này ai mà giải được

làm ơn giúp e vs

\(1,=\left(x-2\right)\left(5-y\right)\\ 2,=2\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(2x-2y-z\right)\\ 3,=5xy\left(x-2y\right)\\ 4,=3\left(x^2-2xy+y^2-4z^2\right)=3\left[\left(x-y\right)^2-4z^2\right]\\ =3\left(x-y-2z\right)\left(x-y+2z\right)\\ 5,=\left(x+2y\right)^2-16=\left(x+2y-4\right)\left(x+2y+4\right)\\ 6,=-\left(6x^2-3x-4x+2\right)=-\left(2x-1\right)\left(3x-2\right)\\ 7,=\left(2x+y\right)\left(2x+y+x\right)=\left(2x+y\right)\left(3x+y\right)\\ 8,=\left(x-y\right)\left(x+5\right)\\ 9,=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\\ 10,=\left(x^2-9\right)x=x\left(x-3\right)\left(x+3\right)\\ 11,=\left(x-2\right)\left(y+1\right)\\ 12,=\left(x-3\right)\left(x^2-4\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\\ 13,=3\left(x+y\right)-\left(x+y\right)^2=\left(x+y\right)\left(3-x-y\right)\)

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

b) \(9-x^2-2xy-y^2=9-\left(x^2+2xy+y^2\right)=9-\left(x+y\right)^2=\left(3-x-y\right)\left(3+x+y\right)\)

c) \(25-x^2+4xy-4y^2=25-\left(x^2-4xy+4y^2\right)=25-\left(x-2y\right)^2=\left(5-x+2y\right)\left(5+x-2y\right)\)

a. x² - 2xy + y² - 1

= (x - y)² - 1²

= (x - y - 1)(x - y + 1)

b. 9 - x² - 2xy - y²

= 3² - (x + y)²

= (3 - x - y)(3 + x + y)

c. 25 - x² + 4xy - 4y²

= 5² - \(\left[x^2-4xy+\left(2y\right)^2\right]\)

= 5² - (x - 2y)²

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

c: \(=\left(5x-y\right)\left(5x+y\right)\)

e: \(=\left(x-2\right)\left(x-3\right)\)

a) x(4y-10x)

b)3(x+2y)+(x+1)

c)(5x-y)(5x+y)

d)5x(y-z)²

e)(x-3)(x-2)

f)(2x+y)³