The sum of two polynomials is 10a2b2 – 8a2b 6ab2 – 4ab 2. if one addend is –5a2b2 12a2b – 5, what is the other addend?
Answer:
The other addend is \(15a^2b^2-20a^2b+6ab^2-4ab+7\).
Step-by-step explanation:
Let the two polynomial are A and B.
One addend is
\(A=-5a^2b^2+12a^2b-5\)
The sum of two polynomials is
\(A+B=10a^2b^2-8a^2b+6ab^2-4ab+2\)
Subtract polynomial A from both the sides.
\(B=10a^2b^2-8a^2b+6ab^2-4ab+2-A\)
\(B=10a^2b^2-8a^2b+6ab^2-4ab+2-(-5a^2b^2+12a^2b-5)\)
\(B=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5\)
Combine like terms.
\(B=(10a^2b^2+5a^2b^2)+(-8a^2b-12a^2b)+6ab^2-4ab+(2+5)\)
\(B=15a^2b^2-20a^2b+6ab^2-4ab+7\)
Therefore the other addend is \(15a^2b^2-20a^2b+6ab^2-4ab+7\).