Question

use the expression below to complete the following tasks.
$(3a^2 - 5ab + b^2) - (-3a^2 + 2b^2 + 8ab)$
what is the additive inverse of the polynomial being subtracted?

• $-3a^2 - 2b^2 - 8ab$
• $-3a^2 + 2b^2 - 8ab$
• $3a^2 - 2b^2 - 8ab$
• $3a^2 + 2b^2 + 8ab$

Explanation:

Step1: Identify the polynomial being subtracted

The expression is \((3a^{2}-5ab + b^{2})-(-3a^{2}+2b^{2}+8ab)\), so the polynomial being subtracted is \(-3a^{2}+2b^{2}+8ab\).

Step2: Find the additive inverse

The additive inverse of a polynomial \(P\) is \(-P\). So we need to find \(-(-3a^{2}+2b^{2}+8ab)\).

Using the distributive property of multiplication over addition (i.e., \(-(x + y+z)=-x - y - z\)), we have:

\(-(-3a^{2}+2b^{2}+8ab)=3a^{2}-2b^{2}-8ab\)

Answer:

C. \(3a^{2}-2b^{2}-8ab\)