a)\(ax-by+bx-ay\)

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

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

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

b) sai đề

a) ax - by + ay - bx

= (ax+ay) - (bx + by)

= a (x+y) - b (x+y)

= (x+y) (a-b)

b) am + bn +bm + an - m - n

= (am + bm - m) + (bn +an -n)

=m (a +b - 1) + n (a + b - 1 )

= (m+n) ( a + b -1)

a/ \(x\left(a+b\right)+y\left(a+b\right)=\left(x+y\right)\left(a+b\right)\)

b/ \(a\left(x+y\right)+b\left(x+y\right)-1\left(x+y\right)=\left(a+b-1\right)\left(x+y\right)\)

c/ \(=x^2z\left(x+y-z-yz\right)\)

a) ko bt làm

a/ \(ab-2b-3a+6=\left(ab-2b\right)-\left(3a-6\right)=b\left(a-2\right)-3\left(a-2\right)=\left(a-2\right)\left(b-3\right)\)

b/ \(ax-by-ay+bx==\left(ax+bx\right)-\left(by+ay\right)=x\left(a+b\right)-y\left(b+a\right)=\left(a+b\right)\left(x-y\right)\)

c/ \(ax+by-ay-bx=\left(ax-ay\right)+\left(by-bx\right)=a\left(x-y\right)+b\left(y-x\right)=a\left(x-y\right)-b\left(x-y\right)=\left(x-y\right)\left(a-b\right)\)

d/ \(a^2-\left(b+c\right)a+bc=a^2-ab-ac+bc=\left(a^2-ac\right)+\left(ab-bc\right)=a\left(a-c\right)+b\left(a-c\right)=\left(a-c\right)\left(a+b\right)\)e/ \(\left(3a-2\right)\left(4a-3\right)-\left(2-3a\right)\left(3a+1\right)=\left(3a-2\right)\left(4a-3\right)+\left(3a-2\right)\left(3a+1\right)=\left(3a-2\right)\left(4a-3+3a+1\right)=\left(3a-2\right)\left(7a-2\right)\)

f/ \(ax+ay+az-bx-by-bz-x-y-z=\left(ax+ay+az\right)-\left(bx+by+bz\right)-\left(x+y+z\right)\)

\(=a\left(x+y+z\right)-b\left(x+y+z\right)-\left(x+y+z\right)=\left(x+y+z\right)\left(a-b-1\right)\)

ax-bx-cx+dx

=x(a-b-c+d)

ax+by+bx+ay

: Trước hết viết lại điều này như sau: 

rìu + bx-by-ay 

Bây giờ phân chia hai thuật ngữ đầu tiên và hai thuật ngữ cuối cùng: 

x (a + b) - y (b + a) 

= x (a + b) - y (a + b) 

Loại bỏ (a + b) như là một yếu tố chung: 

= (a + b) (x - y). 

ax-bx-cx+dx=x.(a-b-c+d)

ax+by+bx+ay=(ax+ay)+(bx+by)=a.(x+y)+b.(x+y)=(a+b).(x+y)

a) ab+bd-ac-cd

= (ab + bd) - (ac + cd)

= b(a+d) - c(a+d)

= (b-c)(a+d)

b) ax+by-ay-bx

= (ax - ay) - (bx - by)

= a(x-y) - b(x-y)

= (a-b)(x-y)

c) x²-xy-xy+y²

= x^2 - 2xy + y^2

= (x-y)^2

\(a,=x^2-mx-nx+mn=x\left(x-m\right)-n\left(x-m\right)=\left(x-n\right)\left(x-m\right)\\ b,=a\left(x-y\right)-b\left(x-y\right)+\left(a-b\right)\\ =\left(x-y\right)\left(a-b\right)+\left(a-b\right)=\left(a-b\right)\left(x-y+1\right)\)

b: \(=a\left(x-y\right)-b\left(x-y\right)+a-b\)

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

a) \(x^2-\left(m+n\right)x+mn=\left(x^2-n\cdot x\right)-\left(m\cdot x-m\cdot n\right)=x\left(x-n\right)-m\left(x-n\right)=\left(x-m\right)\left(x-n\right)\)

b) \(ax+by+a-bx-ay-b\)

   \(=\left(ax-ay+a\right)-\left(bx-by+b\right)\)

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

   \(\left(a-b\right)\left(x-y+1\right)\)