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

Question

1761 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-11T04:20:21

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

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 · 2017-10-11T04:22:10

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

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

#(-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#

We can further factorise this as :

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

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

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