dấu '^' ý là mũ hả p

\(=\dfrac{2x\left(x-2y\right)}{\left(x+2y\right)^2}\cdot\dfrac{\left(x-2y\right)^2}{-\left(x-2y\right)\left(x+2y\right)}:\dfrac{5x^2y-10xy^2}{x^3+6x^2y+12xy^3+8y^3}\)

\(=\dfrac{-2x\left(x-2y\right)^2}{\left(x+2y\right)^3}\cdot\dfrac{\left(x+2y\right)^3}{5xy\left(x-2y\right)}\)

\(=\dfrac{-2x\cdot\left(x-2y\right)}{5xy}=\dfrac{-2\left(x-2y\right)}{5y}\)

a) 4x² + 12xy² = 4x.(x+3y²)

b) 3x³y² - 9x²y² +15x²y = 3x²y.(xy - 3y +5)

c) 10x.(x-y) + 5y.(x-y) = 5.(x-y).(2x+y)

d) x² + 4xy - 16 + 4y²

= (x+2y)² - 16

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

e) 3x² + 5y - 3xy - 5x

= 3x.(x-y) - 5.(x-y)

= (x-y).(3x-5)

g) 5x² -10xy + 5y² - 20z²

= 5.(x² -2xy + y² - 4z² )

= 5.[ (x-y)² - 4z² ]

= 5.(x-y-4z).(x-y+4z)

câu h đề giống câu d nha bn

Bạn xem lại đề câu d nhé.

D=x^2+5y^2-4xy-6x+8y+12

Trả lời:

a, 5x² + 10xy + 5y² = 5 ( x² + 2xy + y² ) = 5 ( x + y )² 

b, x² + 3x - y² + 3y = ( x² - y² ) + ( 3x + 3y ) = ( x - y )( x + y ) + 3 ( x + y ) = ( x + y )( x - y + 3 )

c, x² + 5x - y² + 5y = ( x² - y² ) + ( 5x + 5y ) = ( x - y )( x + y ) + 5 ( x + y ) = ( x + y )( x - y + 5 )

d, 3x² - 3y² - 2 ( x - y )² = 3 ( x² - y² ) - 2 ( x - y )² = 3 ( x - y )( x + y ) - 2 ( x - y )² = ( x - y )[ 3 ( x + y ) - 2 ] = ( x - y )( 3x + 3y - 2 )

e, x² - 2x - 4y² - 4y = ( x² - 4y² ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2 ( x + 2y ) = ( x + 2y )( x - 2y - 2 )

a) 5x²+10xy+5y²

=5(x²+2xy+y²)

=5(x+y)²

b) x²+3x-y²+3y

=(x²-y²)+(3x+3y)

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

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

c) x²+5x-y²+5y

=(x²-y²)+(5x+5y)

=(x-y)(x+y)+5(x+y)

=(x+y)(x-y+5)

d) 3x²-3y²-2(x-y)²

=3(x²-y²)-2(x-y)²

=3(x-y)(x+y)-2(x-y)²

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

e) x²-2x-4y²-4y

=(x²-4y²)-(2x+4y)

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

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

#H

a) 25x² - y² + 4y - 4 

= (5x)² - (y - 2)² 

= (5x + y - 2)(5x - y + 2)

b) a² + b² - x² - y² + 2ab - 2xy 

= (a² + 2ab + b²) - (x² + 2xy + y²)

= (a + b)² - (x + y)²

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

c) 5x²(x - 1) + 10xy(x - 1) - 5y²(1 - x)

= 5x²(x - 1) + 10xy(x - 1) + 5y²(x - 1)

= (x - 1)(5x² + 10xy + 5y²)

= 5(x - 1)(x² + 2xy + y²) 

= 5(x -1)(x  + y)²

d) x⁵ - x⁴y - xy⁴ + y⁵

= x⁴(x - y) - y⁴(x - y)

= (x - y)(x⁴ - y⁴) 

= (x - y)(x² - y²)(x² + y²) = (x - y)²(x + y)(x² + y²) 

Chu choa, đi hỏi khắp nơi luôn kìa trời!

a) Ta có: \(5x\left(x-9\right)-x+9\)

\(=5x\left(x-9\right)-\left(x-9\right)\)

\(=\left(x-9\right)\left(5x-1\right)\)

b) Ta có: \(6x^2+7x-3\)

\(=6x^2+9x-2x-3\)

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

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

d) Ta có: \(x^2-10xy+25y^2\)

\(=x^2-2\cdot x\cdot5y+\left(5y\right)^2\)

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

a: \(\dfrac{9x^3y^2-4xy^2+5x}{2x}=\dfrac{9}{2}x^2y^2-2y^2+\dfrac{5}{2}\)

b: \(\left(\dfrac{3}{4}x^3y^6+\dfrac{6}{5}x^4y^3-\dfrac{9}{10}x^5y\right):\dfrac{-3}{5}x^3y\)

\(=y^5\cdot\left(\dfrac{3}{4}:\dfrac{-3}{5}\right)-xy^2\cdot\left(\dfrac{6}{5}:\dfrac{3}{5}\right)+\dfrac{9}{10}:\dfrac{3}{5}\cdot x^2\)

\(=\dfrac{-5}{4}y^5-2xy^2+\dfrac{3}{2}x^2\)