a. 7x⁵ - 14x³y + 21x²y

= 7x²(x³ - 2xy + 3y)

b. 4x² - 20x + 25

= (2x)² - 2x.2.5 + 5²

= (2x - 5)²

a) \(7x^5-14x^3y+21x^2y\)

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

b) \(4x^2-20x+25\)

\(=\left(2x\right)^2-2.2x.5+5^2\)

\(\left(2x-5\right)^2\)

a: =x^3(x-y)+(x-y)

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

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

b: =(a-1)^2-9b^2

=(a-1-3b)(a-1+3b)

b: \(\left(xy-8\right)^2-1\)

\(=\left(xy-8\right)^2-1^2\)

\(=\left(xy-8-1\right)\left(xy-8+1\right)\)

=(xy-7)(xy-9)

a: \(xy+y^2-x-y\)

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

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

`#3107.10117`

2 a, xy + y^2 - x - y
= (xy + y^2 ) - (x + y)
= y( x + y ) - ( x + y )
= ( x + y ) ( y - 1 )

Lời giải:
a.

$7-3a=(\sqrt{7}-\sqrt{3a})(\sqrt{7}+\sqrt{3a})$

b. 

$14x^2-11=(\sqrt{14}x-\sqrt{11})(\sqrt{14}x+\sqrt{11})$

c.

$3x-6\sqrt{x}-6=3(x-2\sqrt{x}-2)$
$=3[(\sqrt{x}-1)^2-3]$

$=3(\sqrt{x}-1-\sqrt{3})(\sqrt{x}-1+\sqrt{3})$

d.

$x\sqrt{x}-3\sqrt{x}-2=x\sqrt{x}-2x+2x-4\sqrt{x}+\sqrt{x}-2$
$=x(\sqrt{x}-2)+2\sqrt{x}(\sqrt{x}-2)+(\sqrt{x}-2)$

$=(\sqrt{x}-2)(x+2\sqrt{x}+1)$

$=(\sqrt{x}-2)(\sqrt{x}+1)^2$

a) \(x-4\sqrt{x-2}+2\left(x\ge2\right)\) 

\(=x-4\sqrt{x-2}-2+4\)

\(=\left(x-2\right)-4\sqrt{x-2}+4\)

\(=\left(\sqrt{x-2}\right)^2-2\cdot2\cdot\sqrt{x-2}+2^2\)

\(=\left(\sqrt{x-2}-2\right)^2\)

b) \(x+4\sqrt{x-2}+2\left(x\ge2\right)\)

\(=x+4\sqrt{x-2}+4-2\)

\(=\left(x-2\right)+4\sqrt{x-2}+4\)

\(=\left(\sqrt{x-2}\right)^2+2\cdot2\cdot\sqrt{x-2}+2^2\)

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

Cưu là mình vs (x^2+x)^2-2(x^2+x)-15

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

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

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

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

`-x^2 +7x-6`

`=-x^2 +6x+x-6`

`=x(6-x)-(6-x)`

`=(x-1)(6-x)`

=-(x^2-7x+6)

=-(x-1)(x-6)

a) \(4\left(x+y\right)\)

b) \(\left(x-3y\right)^2\)

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

a) \(4 (x + y)\)

b) \((x - 3y)^2\)

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

a: \(=\left(x+1\right)\left(x^2-x+1\right)+5x\left(x+1\right)\)

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