Question

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9. What should be added to x2 - y2 + 2xy to obtain x2 + y2 + 5xy?
10. What should be subtracted from - 7mn + 2m2 + 3n2 to get m2 + 2mn + n2?
11. How much is ys - 12y2 + y + 14 greater than 17y3 + 34y2 - 51y + 68?
12. How much does 93 p2 - 55p + 4 exceed 13p3 - 5p2 + 17p - 90?
13. What should be taken away from 3x2 – 4y2 + 5xy + 20 to obtain - x2 - y2 + xy + 20?
14. From the sum of 2y2 + 3yz, - y - yz - z2 and yz + 222, subtract the sum of 3y2 - 32
and - y2 + y2 + z2​

Answer 1

Question :  What should be added to x² - y² + 2xy to obtain x² + y² + 5xy

What should be subtracted from - 7mn + 2m² + 3n² to get m² + 2mn + n²

Solution:

let say A be added to x² - y² + 2xy to obtain x² + y² + 5xy

=> A + x² - y² + 2xy = x² + y² + 5xy

=> A = x² + y² + 5xy  - ( x² - y² + 2xy )

=> A = x² + y² + 5xy  - x² + y² - 2xy

=> A = 2y² + 3xy

2y² + 3xy should be added to x² - y² + 2xy to obtain x² + y² + 5xy

Let Say A be subtracted from - 7mn + 2m² + 3n² to get m² + 2mn + n²

=> - 7mn + 2m² + 3n²  - A  = m² + 2mn + n²

=>  - 7mn + 2m² + 3n²  - ( m² + 2mn + n²) = A

=> - 7mn + 2m² + 3n²  - m² - 2mn - n²  = A

=> m² + 2n²  - 9mn = A

m² + 2n²  - 9mn should be subtracted from - 7mn + 2m² + 3n² to get m² + 2mn + n²

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