Question

1)what should be added to x²+xy+y²to obtain 2x²+3xy?

2)why should be subtracted from 2a+8b+10to get -3a+7b+16?​

Answer 1

Answer:

(1)

Let the number which should added be "Z"

$x {}^{2} + xy + y {}^{2} + z = 2x {}^{2} + 3xy \\ z = 2x {}^{2} - x {}^{2} - y {}^{2} + 3xy - xy \\ z = {x}^{2} - y {}^{2} + 2y$

(2)

let the number which should be subtracted be "Z"

$z - (2a + 8b + 10) = - 3a + 7b + 16 \\ z - 2a - 8b - 10 = - 3a + 7b + 16 \\ z = 2a - 3a + 8b + 7b + 10 + 16 \\ z = - a + 15b + 26$

Answer 2

1)

Let the number which should added be "Z"

x {}^{2} + xy + y {}^{2} + z = 2x {}^{2} + 3xy \\ z = 2x {}^{2} - x {}^{2} - y {}^{2} + 3xy - xy \\ z = {x}^{2} - y {}^{2} + 2y

(2)

let the number which should be subtracted be "Z"

z - (2a + 8b + 10) = - 3a + 7b + 16 \\ z - 2a - 8b - 10 = - 3a + 7b + 16 \\ z = 2a - 3a + 8b + 7b + 10 + 16 \\ z = - a + 15b + 26