\(ab\left(x^2+y^2\right)-xy\left(a^2+b^2\right)\)

\(=abx^2+aby^2-a^2xy-b^2xy\)

\(=\left(abx^2-b^2xy\right)-\left(a^2xy-aby^2\right)\)

\(=bx\left(ax-by\right)-ay\left(ax-by\right)\)

\(=\left(ax-by\right)\left(bx-ay\right)\)

a: \(x^4+25x^2+20x-4\)

\(=x^4-5x^3+2x^2+5x^3-25x^2+10x-2x^2+10x-4\)

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

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

b: \(=x^4-6x^2-x^2+9\)

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

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

c: \(=abx^2+aby^2-a^2xy-b^2xy\)

\(=\left(abx^2-b^2xy\right)+\left(aby^2-a^2xy\right)\)

\(=xb\left(ax-by\right)+ay\left(by-ax\right)\)

\(=\left(ax-by\right)\cdot\left(xb-ay\right)\)

\(3,x\left(x-1\right)-y\left(1-x\right)=\left(x+y\right)\left(x-1\right)\\ 4,x^3+6x^2y+12xy^2+8y^3=\left(x+2y\right)^3\\ 5,x^2-2xy+y^2-xz+yz=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y-z\right)\left(x-y\right)\\ 6,x^2-y^2-x+y=\left(x-y\right)\left(x+y\right)-\left(x-y\right)=\left(x-y\right)\left(x+y-1\right)\\ 9,x^3+x^2-xy+xy+y^2+y^3\\ =x^2\left(x+1\right)+y^2\left(x+1\right)=\left(x^2+y^2\right)\left(x+1\right)\\ 10,x^2-6\left(x+3\right)-9\\ =x^2-6x-18-9\\ =x^2-6x-27=\left(x-9\right)\left(x+3\right)\)

10: \(x^2-6\left(x+3\right)-9\)

\(=x^2-6x-18-9\)

\(=x^2-6x-27\)

\(=\left(x-9\right)\left(x+3\right)\)

3)(x-1).(x-y)

a)

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

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

b)

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

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

c)

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

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

d)

\(=x^3\left(x-2\right)+10x\left(x-2\right)\)

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

e)

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

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

f)

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

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

a,2x³+3x²+2x+3

=(2x³+2x)+(3x²+3)

=2x(x²+1)+3(x²+1)

=(x²+1)(2x+3)

b,a²-ab+a-b

=(a²-ab)+(a-b)

=a(a-b)+(a-b)

=(a-b)(a+1)

c,2x²+4x+2-2y²

=2(x²+2x+1-y²)

=2[(x²+2x+1)-y² ]

=2[(x+1)²-y² ]

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

d,x⁴-2x³+10x²-20x

=(x⁴-2x³)+(10x²-20x)

=x³(x-2)+10x(x-2)

=(x-2)(x³+10x)

=(x-2)[x(x²+10)]

e,x³+2x²+x

=x(x²+2x+1)

=x(x+1)²

f,xy+y²-x-y

=(xy+y²)-(x-y)

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

=(x+y)(y-1)

x² - x - y² - y

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

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

***

9x² + y² - 16z² + 6xy

= (3x + y)² - (4z)²

= (3x + y - 4z)(3x + y + 4z)

***

a³ - a²x - ay + xy

= a²(a - x) - y(a - x)

= (a - x)(a² - y)

***

2x² - 8y² + 3x + 6y

= 2(x² - 4y²) + 3(x + 2y)

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

= (x + 2y)(2x - 4y + 3)

***

xy(x + y) + yz(y + z) + xz(x + z) + 2xyz

= xy(x + y + z) + yz(x + y + z) + xz(x + z)

= y(x + y + z)(x + z) + xz(x + z)

= (x + z)(xy + y² + yz + xz)

= (x + z)[y(x + y) + z(x + y)]

= (x + z)(x + y)(y + z) 

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

x²y-xy²-3x+3y

=(x²y-xy²)-(3x-3y)

=xy(x-y)-3(x-y)

=(x-y).(xy-3)

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

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

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

d) \(y^2\left(x-1\right)-7y^3+7xy^3\)

\(=y^2\left(x-1-7y+7xy\right)\)

\(=y^2\left[\left(x-1\right)-7y\left(1-x\right)\right]=y^2\left(x-1\right)\left(1+7y\right)\)

a)

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

b)

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

bài 2 :

0,25x³+x²+x=0

<=>0,25x³+0,5x²+0,5x²+x=0

<=>0,25x²(x+2)+0,5x(x+2)=0

<=>(x+2)(0,25x²+0,5x)=0

<=>(x+2)x(0,25x+0,5)=0

<=>x+2=0 hoặc x=0 hoặc 0,25x+0,5=0

=>x=-2 hoặc x=0 hoặc x=-2

vậy x=0 hoặc x=-2