a) x2 + xy –x – y = x(x + y) – (x + y) = (x + y)(x -1 ).

b) a2 – b2 + 8a + 16 = (a2 + 8a + 16) – b2 = (a + 4)2 – b2

= (a + 4 – b)(a + 4 + b).

a)3y(x² -2xy+y)

b)=(a+b)(a-b)+2(a+b)

=(a+b)(a-b+2)

b)

a, \(4abc-8ab^2c=4abc\left(1-2b\right)\)

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

\(=x\left(x-1\right)\left(2a-1\right)\)

c, \(9a^4\left(a-2\right)+a^2\left(a-2\right)=a^2\left(9a^2+1\right)\left(a-2\right)\)

d, \(\left(a-4\right)\left(2a-1\right)-8a+4=\left(a-4\right)\left(2a-1\right)-4\left(2a-1\right)\)

\(=\left(a-8\right)\left(2a-1\right)\)

a) `4abc-8ab^2c=4abc(1-2b)`

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

c) `9a^4 (a-2) +a^2 (a-2) = (a-2)(9a^4+a^2)=a^2 (a-2)(9a^2+1)`

d) `(a-4)(2a-1)-8a+4=(a-4)(2a-1)-4(2a-1)=(2a-1)(a-8)`

\(a,=5x\left(x-1\right)+y\left(x-1\right)=\left(5x+y\right)\left(x-1\right)\\ b,=\left(x-y\right)^2-9=\left(x-y-3\right)\left(x-y+3\right)\)

a)5x²-5x+xy-y=(5x²-5x)+(xy-y)=5x(x-1)+y(x-1)=(x-1)(5x+y)

b)x²-2xy+y²-9=(x²-2xy+y²)-9=(x-y)²-3²=(x-y-3)(x-y+3)

a) x²y+xy+x+1= (x²y+xy)+(x+1)=xy(x+10+(x+1)=(x+1)(xy+1)

b) x²-(a+b)x+ab=x²-ax-bx+ab=(x²-ax)-(bx-ab)=x(x-a)-b(x-a)=(x-a)(x-b)

c) ax²+ay-bx²-by=(ax²+ay)-(bx²+by)=a(x²+y)-b(x²+y)=(a-b)(x²+y)

d) ax-2x-a²+2a=(ax-2x)-(a²-2a)=x(a-2)-a(a-2)=(a-2)(x-a)

e) 2x²+4ax+x+2a=(2x²+4ax)+(x+2a)=2x(x+2a)+(x+2a)=(x+2a)(2x+1)

f) x³+ax²+x+a=(x³+ax²)+(x+a)=x²(x+a)+(x+a)=(x²+1)(x+a)

g: Ta có: \(x^4+2x^3-4x-4\)

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

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

\(a.x^3-2x^2-2x-4\\ =\left(x^3-2x^2\right)-\left(2x-4\right)\\ =x^2\left(x-2\right)-2\left(x-2\right)\\ =\left(x^2-2\right)\left(x-2\right)\)

\(b.xy+1-x-y\\ =\left(xy-x\right)+\left(-y+1\right)\\ =x\left(y-1\right)-\left(y-1\right)\\ =\left(x-1\right)\left(y-1\right)\)

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

\(d.16-x^2+2xy-y^2\\ =4^2-\left(x-y\right)^2\\ =\left(4-x+y\right)\left(4-x-y\right)\)

b: =xy-x-y+1

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

=(x-1)(y-1)

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

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

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

=16-(x-y)^2

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

b: \(=\left(x-y\right)^2-4y^2\)

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

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

c: \(=x\left(x-6\right)+y\left(x-6\right)\)

\(=\left(x-6\right)\left(x+y\right)\)

từng câu 1 thôi:v

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

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