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

a) \(24x^2-4xy\)

\(=4x\left(6x-y\right)\)

b) \(5x^3-10x^2+5x-20xy^2\)

\(=5x\left(x^2-10x+5-20y^2\right)\)

nhầm câu b nha 

\(5x^3-10x^2+5x-20xy^2\)

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

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

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

     y^2 - ( x^2 - 2x + 1 )

⇔ y^2 - ( x - 1 )^2

⇔ ( y - x - 1 ) ( y + x - 1 )

nha bạn 

  ( x + y )² - 2( x + y ) + 1 = 

= ( x + y - 1 )² ( áp dụng hằng đẳng thức thứ bình phương 1 hiệu nha )

Hok tốt!!!!!!!!!!!!!!!!

(x+y)²-2(x+y)+1

=(x+y)²-2.(x+y).1+1²

=(x+y-1)²

\(c,Sửa:\dfrac{1}{4x+2}=\dfrac{x\left(2x-1\right)}{2x\left(2x+1\right)\left(2x-1\right)}\\ \dfrac{20}{4x^3-x}=\dfrac{40}{2x\left(2x+1\right)\left(2x-1\right)}\\ \dfrac{7}{2x^2+x}=\dfrac{7\left(2x-1\right)}{x\left(2x+1\right)\left(2x-1\right)}\\ d,\dfrac{x}{x-y};\dfrac{x^2-y^2}{x^2-2xy+y^2}=\dfrac{\left(x-y\right)\left(x+y\right)}{\left(x-y\right)^2}=\dfrac{x+y}{x-y};x+y=\dfrac{x^2-y^2}{x-y}\\ e,\dfrac{x}{x+1}=\dfrac{x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)};\dfrac{x^2}{1-x}=\dfrac{-x^2\left(x+1\right)}{\left(x+1\right)\left(x-1\right)};\dfrac{1}{x^2-1}=\dfrac{1}{\left(x-1\right)\left(x+1\right)}\)

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

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

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

a: \(5x-20y=5\left(x-4y\right)\)

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

c: \(x\left(x+y\right)-\left(5x+5y\right)=\left(x+y\right)\left(x-5\right)\)

d: \(5\left(x-y\right)+y\left(x-y\right)=\left(x-y\right)\left(y+5\right)\)

\(2x^2+5x-3=\left(2x^2-x\right)+\left(6x-3\right)\)\(=x\left(2x-1\right)+3\left(2x-1\right)=\left(x+3\right)\left(2x-1\right)\)

2x²+5x-3

=2x²-x+6x-3

=x(2x-1)+3(2x-1)

=(x+3)(2x-1)

dễ lém nha:

2x²+5x-3=2x²-x+6x-3

             =x(2x-1)+3(2x-1)

             =(x+3)(2x-1)