Question

(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

(b) What should be subtracted from 2a + 8b + 10 to get − 3a + 7b + 16?

Answer 1

(a) Let a be the required term.

a + (x² + y² + xy) = 2x² + 3xy
a = 2x² + 3xy − (x² + y² + xy)

a = 2x² + 3xy − x² − y² − xy

a = 2x² − x² − y² + 3xy − xy

= x² − y² + 2xy
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(b) Let p be the required term.

(2a + 8b + 10) − p = − 3a + 7b + 16

p = 2a + 8b + 10 − (− 3a + 7b + 16)

= 2a + 8b + 10 + 3a − 7b − 16

= 2a + 3a + 8b − 7b + 10− 16

= 5a + b − 6