Question

finding a missing polynomial addend

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?

(15a^2b^2 - 20a^2b + 6ab^2 - 4ab + 7)
(5a^2b^2 - 20a^2b^2 + 7)
(5a^2b^2 + 4a^2b^2 + 6ab - 4ab - 3)
(-15a^2b^2 + 20a^2b^2 - 6ab + 4ab - 7)

Explanation:

Set up the subtraction equation

$$ P_{\text{other}} = (10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2) - (-5a^2b^2 + 12a^2b - 5) $$

Distribute the negative sign

$$ P_{\text{other}} = 10a^2b^2 - 8a^2b + 6ab^2 - 4ab + 2 + 5a^2b^2 - 12a^2b + 5 $$

Combine like terms

$$
LATEXBLOCK0
$$

Answer:

• (A) \(15a^2b^2 - 20a^2b + 6ab^2 - 4ab + 7\) (Correct answer)
• (B) \(5a^2b^2 - 20a^2b^2 + 7\)
• (C) \(5a^2b^2 + 4a^2b^2 + 6ab - 4ab - 3\)
• (D) \(-15a^2b^2 + 20a^2b^2 - 6ab + 4ab - 7\)