What should be taken away from 3x2 – 4y2 + 5xy +20 to get – x2

1.	What should be taken away from 3x2 – 4y2 + 5xy +20 to get – x2 – y2 + 6xy + 20.
Answer» Let the subtracted algebraic expression may be B’ say 3x² – 4y² + 5xy – B = – x² – y² + 6xy + 20 B = (3x² – 4y² + 5xy) – (- x² – y² + 6xy + 20) = 3x² – 4y² + 5xy + x² +y² – 6xy – 20 = (3x² + x²) ( – 4y² + y²) + (5xy – 6xy) – 20 ∴ B = 4x² – 3y² – xy – 20 ∴ The required subtracted expression is B = 4x² – 3y² – xy – 20

What should be taken away from 3x2 – 4y2 + 5xy +20 to get – x2 – y2 + 6xy + 20.

Answer»

Let the subtracted algebraic expression may be B’ say

3x² – 4y² + 5xy – B = – x² – y² + 6xy + 20

B = (3x² – 4y² + 5xy) – (- x² – y² + 6xy + 20)

= 3x² – 4y² + 5xy + x² +y² – 6xy – 20

= (3x² + x²) ( – 4y² + y²) + (5xy – 6xy) – 20

∴ B = 4x² – 3y² – xy – 20

∴ The required subtracted expression is B

= 4x² – 3y² – xy – 20