Question

the sum of two polynomials is $10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2$. if one addend is $-5a^2b^2 + 12a^2b - 5$, what is the other addend?
\bigcirc $15a^2b^2 - 20a^2b + 6ab^2 - 4ab + 7$
\bigcirc $5a^2b^2 - 20a^2b^2 + 7$
\bigcirc $5a^2b^2 + 4a^2b^2 + 6ab - 4ab - 3$
\bigcirc $-15a^2b^2 + 20a^2b^2 - 6ab + 4ab - 7$

Explanation:

Step1: Set up subtraction

To find the other addend, subtract the given addend from the total sum:
$$(10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2) - (-5a^2b^2 + 12a^2b - 5)$$

Step2: Distribute the negative sign

Flip the sign of each term in the second polynomial:
$$10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2 + 5a^2b^2 - 12a^2b + 5$$

Step3: Combine like terms

Group and add/subtract terms with identical variables:

• For $a^2b^2$: $10a^2b^2 + 5a^2b^2 = 15a^2b^2$
• For $a^2b$: $-8a^2b - 12a^2b = -20a^2b$
• For $ab^2$: $6ab^2$ (no like terms)
• For $ab$: $-4ab$ (no like terms)
• Constants: $2 + 5 = 7$

Combine all results:
$$15a^2b^2 - 20a^2b + 6ab^2 - 4ab + 7$$

Answer:

A. $15a^2b^2 - 20a^2b + 6ab^2 - 4ab + 7$