1) \(=\left(3x^2y-3xy^2\right)+\left(5x-5y\right)=3xy\left(x-y\right)+5\left(x-y\right)=\left(x-y\right)\left(3xy+5\right)\)

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

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

1) \(3x^2y-5y-3xy^2+5x\)

\(=3xy\left(x-y\right)+5\left(x-y\right)\)

\(=\left(3xy+5\right)\left(x-y\right)\)

2) \(ax+by+ay+bx\)

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

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

3) \(x\left(x-2y\right)-x+2y\)

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

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

d. 2x²(x - y) + 2y(y - x)

= 2x²(x - y) - 2y(x - y)

= (2x² - 2y)(x - y)

= 2(x² - y)(x - y)

e. 5a²b(a - 2b) - 2a(2b - a)

= 5a²b(a - 2b) + 2a(a - 2b)

= (5a²b + 2a)(a - 2b)

= a(5ab + 2)(a - 2b)

f. 4x²y(x - y) + 9xy²(x - y)

= (4x²y + 9xy²)(x - y)

= xy(4x + 9y)(x - y)

g. 50x²(x - y)² - 8y²(y - x)²

= 50x²(x² - 2xy + y²) - 8y²(y² - 2xy + x²)

= 50x²(x² - 2xy + y²) - 8y²(x² - 2xy + y²)

= 50x²(x - y)² - 8y²(x - y)²

= (50x² - 8y²)(x - y)²

= 2(25x² - 4y²)(x - y)².

g: Ta có: \(50x^2\left(x-y\right)^2-8y^2\left(y-x\right)^2\)

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

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

A = 9x² + 6x + 15

A = [(3x + 6x + 1] + 14

A = (3x + 1)² + 14 \(\ge\)14

Dấu = xảy ra \(\Leftrightarrow\)3x + 1 = 0

                        \(\Rightarrow\)3x = - 1

                       \(\Rightarrow\)x = - 1 / 3

Min A = 14 \(\Leftrightarrow\)x = - 1 / 3

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

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

a) \(x^4+x^3-8x-8\)

\(=x^3\left(x+1\right)-8\left(x+1\right)\)

\(=\left(x^3+8\right)\left(x+1\right)\)

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

a) \(=x^3\left(x+1\right)-8\left(x+1\right)=\left(x+1\right)\left(x^3-8\right)=\left(x+1\right)\left(x-2\right)\left(x^2+2x+4\right)\)

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

c) \(=3\left(x-y\right)-a\left(x-y\right)=\left(x-y\right)\left(3-a\right)\)

b) \(xy+2y-3\left(x+2\right)\)

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

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

c) \(3\left(x-y\right)+ay-ax\)

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

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

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

\(\left(x:2,2\right)\times\dfrac{1}{6}=\dfrac{-3}{8}\times\left(0,5-1\dfrac{3}{5}\right)\)

\(\Rightarrow\left(x:2,2\right)\times\dfrac{1}{6}=\dfrac{-3}{8}\times\left(\dfrac{1}{2}-\dfrac{8}{5}\right)\)

\(\Rightarrow\left(x:2,2\right)\times\dfrac{1}{6}=\dfrac{-3}{8}\times\dfrac{11}{10}\)

\(\Rightarrow\left(x:2,2\right)\times\dfrac{1}{6}=\dfrac{33}{80}\)

\(\Rightarrow x:2,2=\dfrac{33}{80}:\dfrac{1}{6}\)

\(\Rightarrow x:2,2=\dfrac{99}{40}\)

\(\Rightarrow x=\dfrac{99}{40}\times2,2\)

\(\Rightarrow x=\dfrac{1089}{200}\)

=>(x:2,2)*1/6=-3/8(1/2-8/5)=33/80

=>x:2,2=99/40

=>x=1089/200