Question

How do you simplify `(-x^2 -9xy +5y2) -(4x^2- 2xy-y^2)`?

Answer 1

`-5x^2-7xy+6y^2`

Explanation:

Your problem is the same as:

`(1)(-x^2-9xy+5y^2)+(-1)(4x^2-2xy-y^2)`

First distribute the `1` and `-1`:

`-x^2-9xy+5y^2-4x^2+2xy+y^2`

Rearrange the terms and show all the coefficients:

`-1x^2-4x^2-9xy+2xy+5y^2+1y^2`

Combine like terms:

`-5x^2-7xy+6y^2`

Answer 2

Simplified `=> -5x^2 -7xy +6y^2`

Factorised form `=> (-5x+3y)(x+2)`

Explanation:

`(-x^2 -9xy +5y2) -(4x^2- 2xy-y^2)`

First open the parenthesis:

`=> -x^2 -9xy +5y2 -4x^2+ 2xy+y^2`

Now group the like terms and solve:

`=> -x^2 - 4x^2- 9xy + 2xy+y^2+5y2`

`=> -5x^2 -7xy +6y^2`

`=> -5x^2 -7xy +6y^2`

We can further factorise this as :

`=> -5x^2-10xy+ 3xy+6y^2`

`=> -5x(x+2y) +3y(x+2y)`

`=> (-5x+3y)(x+2)`