Question

Answer 1

Bài 1A

\(a,=3\left(x-y\right)+\left(x-y\right)\left(x+y\right)\\ =\left(x-y\right)\left(3+x+y\right)\\ b,=\left(x^2+2xy+y^2\right)-4x^2y^2\\ =\left(x+y\right)^2-4x^2y^2=\left(x+y-2xy\right)\left(x+y+2xy\right)\\ c,=x^4\left(x^2-1\right)+2x^2\left(x+1\right)\\ =x^4\left(x+1\right)\left(x-1\right)+2x^2\left(x+1\right)\\ =\left(x+1\right)\left[x^4\left(x-1\right)+2x^2\right]\\ =\left(x+1\right)\left(x^5-x^4+2x^2\right)\\ d,=\left(x-1\right)^3-y^3\\ =\left(x-1-y\right)\left[\left(x-1\right)^2+y\left(x-1\right)+y^2\right]\\ =\left(x-y-1\right)\left(x^2-2x+1+xy-y+y^2\right)\)

Answer 2

1B;

a: =(x+y)+(x+y)(x-y)=(x+y)(x-y+1)

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

d: \(=\left(x+1\right)^3-y^3\)

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

Answer 3

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

b, \(x^2+2xy+y^2-4x^2y^2=\left(x+y\right)^2-4x^2y^2=\left(x+y-2xy\right)\left(x+y+2xy\right)\)

c, \(x^4\left(x^2-1\right)+2x^2\left(x+1\right)=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)=\left(x+1\right)\left(x^5-x^4+2x^3\right)\)

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

Answer 4

a, 3 ( x − y ) + ( x − y ) ( x + y ) = ( x + y + 3 ) ( x − y )

Answer 5

Bài 1A

`a, 3x - 3y +x^2 - y^2`

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

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

`b, x^2 -4x^2y^2 + y^2 + 2xy`

`=(x+y)^2 - 4x^2y^2`

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

`c, x^4(x^2 - 1) + 2x^2(x+1)`

`= x^4(x-1)(x+1) + 2x^2(x+1)`

`= (x+1)(x^5 - x^4 + 2x^2)`

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

`d, (x-1)^3 - y^3`

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

`

Answer 6

Bài `1B`:

`a, x + y + x^2 - y^2`

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

`b, x^2 - 2y -2y^2 + x^2y`

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

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

`d, (x+1)^3 - y^3`

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

 

Answer 7

Bài `2A`:

`3x(x-1) + (x-1) = 0`

`-> (3x +1)(x-1)=0`

`-> x = -1/3` hoặc `x = 1`

`b, (2x-1)^2 - 25 = 0`

`-> (2x-6)(2x+4) =0`

`-> 4(x-3)(x+2) = 0`

`-> x = 3` hoặc `x + 2`

`c, (x+3)(x^2 - 3x + 9) + (x+3)(x-9) = 0`

`-> (x+3)(x^2 -2x) = 0`

`-> x(x+3)(x-2) = 0`

`-> x = 0, -3` hoặc `-2`

`d, 

Answer 8

Bài `2B`:

`a, x(x+1) + x+ 1=0`

`-> (x+1)(x+1) = 0`

`-> (x+1)^2 = 0`

`-> x= -1`

`b, (x+2)^2 - 3^2 = 0`

`-> (x-1)(x+5) = 0`

`-> x = 1` hoặc `-5`

`c, (x+2)(x^2 - 2x + 4) + (x+2)(x+7)= 0`

`-> (x+2)(x^2 - x + 11) =0`

`-> x = -2`