Question

what should be taken away from 3x-4y+5xy+20 to obtain-x-y+6xy+20

Answer 1

Let p be the required term.
(3x2 − 4y2 + 5xy + 20) − p = − x2 − y2 + 6xy + 20
p = (3x2 − 4y2 + 5xy + 20) − (− x2 − y2 + 6xy + 20)
= 3x2 − 4y2 + 5xy + 20 + x2 + y2 − 6xy − 20
= 3x2 + x2 − 4y2 + y2 + 5xy − 6xy + 20 − 20
= 4x2 − 3y2 − xy

Answer 2

let the unknown no. be 'a'
(3x - 4y +5xy+20) - a = - x-y+6xy+20
-a = -x-y+6xy+20 -(3x-4y+5xy+20)
-a = -x-y+6xy+20 -3x+4y-5xy-20
-a = -4x+3y+xy
-a = -(4x-3y-xy)
a = 4x - 3y -xy (cancelling the '-' sign)
therefore 4x - 3y - xy should be taken away.

Hope u understood =D