Question

a)\(x^3-3x^2+1-3x\)

b) \(x^2\text{+4x - 2xy - 4y +}y^2\)

c) \(3x^2-6xy+3y^2-12z^2\)

Answer 1

`a,x^3 - 3x^2 + 1 - 3x`

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

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

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

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

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

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

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

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

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

`c,3x^2 -6xy + 3y^2 - 12z^2`

`=3(x^2 -2xy +y^2 - 4z^2)`

`=3[(x-y)^2 - (2z)^2]`

`=3(x-y-2z)(x-y+2z)`
 

Answer 2

a: =x^3+1-3x^2-3x

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

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

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

b: =x^2-2xy+y^2+4x-4y

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

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

c: =3(x^2-2xy+y^2-4z^2)

=3[(x-y)^2-4z^2]

=3(x-y-2z)(x-y+2z)

Answer 3

a: =x^3+1-3x^2-3x

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

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

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

b: =x^2-2xy+y^2+4x-4y

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

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

c: =3(x^2-2xy+y^2-4z^2)

=3[(x-y)^2-4z^2]

=3(x-y-2z)(x-y+2z)