How do you simplify (-x^2 -9xy +5y2) -(4x^2- 2xy-y^2)(−x2−9xy+5y2)−(4x2−2xy−y2)?

2 Answers
M7chael
Oct 11, 2017

-5x^2-7xy+6y^2−5x2−7xy+6y2

Explanation:

Your problem is the same as:

(1)(-x^2-9xy+5y^2)+(-1)(4x^2-2xy-y^2)(1)(−x2−9xy+5y2)+(−1)(4x2−2xy−y2)

First distribute the 11 and -1−1:

-x^2-9xy+5y^2-4x^2+2xy+y^2−x2−9xy+5y2−4x2+2xy+y2

Rearrange the terms and show all the coefficients:

-1x^2-4x^2-9xy+2xy+5y^2+1y^2−1x2−4x2−9xy+2xy+5y2+1y2

Combine like terms:

-5x^2-7xy+6y^2−5x2−7xy+6y2

Pallu
Oct 11, 2017

Simplified => -5x^2 -7xy +6y^2⇒−5x2−7xy+6y2

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

Explanation:

(-x^2 -9xy +5y2) -(4x^2- 2xy-y^2)(−x2−9xy+5y2)−(4x2−2xy−y2)

First open the parenthesis:

=> -x^2 -9xy +5y2 -4x^2+ 2xy+y^2⇒−x2−9xy+5y2−4x2+2xy+y2

Now group the like terms and solve:

=> -x^2 - 4x^2- 9xy + 2xy+y^2+5y2⇒−x2−4x2−9xy+2xy+y2+5y2

=> -5x^2 -7xy +6y^2⇒−5x2−7xy+6y2

=> -5x^2 -7xy +6y^2⇒−5x2−7xy+6y2

We can further factorise this as :

=> -5x^2-10xy+ 3xy+6y^2⇒−5x2−10xy+3xy+6y2

=> -5x(x+2y) +3y(x+2y)⇒−5x(x+2y)+3y(x+2y)

=> (-5x+3y)(x+2)⇒(−5x+3y)(x+2)

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