Question

Answer 1

Bài 1.5:

a: \(A=5x^2y-10xy^2\)

\(=5xy\cdot x-5xy\cdot2y\)

=5xy(x-2y)

b: \(B=2x^3+6x^2-4x\)

\(=2x\cdot x^2+2x\cdot3x-2x\cdot2\)

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

c: \(C=2x\left(3y-7z\right)+6y\left(7z-3y\right)\)

\(=2x\cdot\left(3y-7z\right)-6y\left(3y-7z\right)\)

\(=\left(3y-7z\right)\left(2x-6y\right)=\left(3y-7z\right)\cdot2\cdot\left(x-3y\right)\)

d: D=2xy(x-y)-x(y-x)

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

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

Bài 1.7:

a: \(A=2xy+6y=2y\cdot x+2y\cdot3=2y\left(x+3\right)\)

b: \(B=-8x^4y^3-12x^2y^4+20x^3y^4\)

\(=-4x^2y^3\cdot2x^2-4x^2y^3\cdot2y+4x^2y^3\cdot5xy\)

\(=-4x^2y^3\left(2x^2+2y-5xy\right)\)

c: \(C=3x^2\left(x+1\right)-2\left(x+1\right)\)

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

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

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

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

\(=\left(x-2y\right)\left(6x-2y\right)=2\left(3x-y\right)\left(x-2y\right)\)

Answer 2

`1`

` A = 5x^2y - 10xy^2`

`=> A = 5xy(x - 2y^2)`

`B = 2x^3 + 6x^2 - 4x`

`=> B = 2x(x^2 + 3x - 2)`

`C = 2x(3y - 7z) + 6y(7z - 3y)`

`= 2x(3y - 7z) - 6y(3y - 7z)`

`=(2x - 6y)(3y - 7z)`

`=2(x - 3y)(3y - 7z)`

`D = 2xy(x-y) - x(y-x)`

`= 2xy(x-y) + x(x-y)`

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

`=x(x-y)(2y+1)`

`2`

`A= 2xy + 6y`

`= 2y(x+3)`

`B=-8x^4y^3 - 12x^2y^4 + 20x^3y^4`

`= -4x^2y^3(2x^2 + 3y -5xy)`

`C = 3x^2(x+1) - 2(x+1)`

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

`D = 5x(x - 2y)  + (2y - x)^2`

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

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

`= (x - 2y)(6x - 2y)`

`= 2(x - 2y)(3x - y)`