Question

Subtract the sum of ( x
² + 2y²
+ 7x

2y ) and ( x
² – 3xy
² ) from the sum of

( x
² – y² – xy ) and ( 3x
² – 2y
² + 7)​

Answer 1

Step: 1

Find the sum of the two equations

(x² + 2y² + 7x) + (x² – 3xy²)

=> x² + 2y² + 7x

+ x² + 0y² + 0x – 3xy²

= 2x² + 2y² + 7x – 3xy²

Step: 2

Find the sum of the next two equations

(x² – y² – xy) + (3x² – 2y² + 7)

=> x² – y² –xy

+ 3x² – 2y² + 0xy + 7

= 4x² – 3y² –xy + 7

Step: 3

Subtract the equation of step 1 from step 2

(4x² – 3y² – xy + 7) – (2x² + 2y² + 7x – 3xy²)

=> 4x² – 3y² – xy + 7 – 2x² – 2y² – 7x + 3xy²

(sign changes)

=> 4x² – 3y² – xy + 7

– 2x² – 2y² – 7x + 3xy²

= 2x² – 5y² – xy + 7 – 7x + 3xy²

= 2x² – 5y² + 3xy² – 7x – xy + 7 (rearranged)

>> 2x² – 5y² + 3xy² – 7x – xy + 7 is the answer