Mathematics
(i) What should be added to 7a - 9b + 13c to get 9a + b - c?
(ii) What should be added to 1 + 2x - 3x2 to get x2 - x - 1?
(iii) What should be added to m2 - 2mn + 5n2 to get n2 + mn - m2?
Algebraic Expressions
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Answer
(i) What should be added to 7a - 9b + 13c to get 9a + b - c?
To find what must be added to A to get B, we simply calculate B - A.
∴ Subtract 7a - 9b + 13c from 9a + b - c:
∴ The required expression is 2a + 10b - 14c
(ii) What should be added to 1 + 2x - 3x2 to get x2 - x - 1?
To find what must be added to A to get B, we simply calculate B - A.
∴ Subtract 1 + 2x - 3x2 from x2 - x - 1:
Arranging the expressions in descending powers of x (x2, x, constant).
∴ The required expression is 4x2 - 3x - 2
(iii) What should be added to m2 - 2mn + 5n2 to get n2 + mn - m2?
To find what must be added to A to get B, we simply calculate B - A.
∴ Subtract m2 - 2mn + 5n2 from n2 + mn - m2
Arranging the terms to match (m2, mn, n2):
∴ The required expression is -2m2 + 3mn - 4n2
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