The sum of two polynomials is 10a2b2 – 8a2b + 6ab2 – 4ab + 2. If one addend is –5a2b2 + 12a2b – 5, what is the other addend?

To find the other addend, subtract the known addend from the sum. Change the signs of −5a²b² + 12a²b − 5, then combine like terms: 10a²b² + 5a²b² = 15a²b², −8a²b − 12a²b = −20a²b, and 2 + 5 = 7. The terms 6ab² and −4ab remain unchanged, giving 15a²b² − 20a²b + 6ab² − 4ab + 7, which is choice A.

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