Question

use the expression below to complete the following tasks. (3a² - 5ab + b²) - (-3a² + 2b² + 8ab) what is the additive inverse of the polynomial being subtracted? -3a² - 2b² - 8ab -3a² + 2b² - 8ab 3a² - 2b² - 8ab 3a² + 2b² + 8ab after you rewrite subtraction as addition of the additive inverse, how can the like terms be grouped? 3a² + (-3a²) + (-5ab + 8ab) + b² + (-2b²) 3a² + (-3a²) + (-5ab + 8ab) + (b² + 2b²) (3a² + 3a²) + -5ab + (-8ab) + b² + (-2b²) (3a² + 3a²) + -5ab + (-2b²) + b² + (-8ab)

Explanation:

Step1: Recall additive inverse concept

The additive inverse of a polynomial \(P(x)\) is \(-P(x)\). The polynomial being subtracted is \(-3a^{2}+2b^{2}+8ab\). Its additive inverse is \(-(-3a^{2}+2b^{2}+8ab)=3a^{2}-2b^{2}-8ab\).

Step2: Rewrite subtraction as addition and group like - terms

The original expression \((3a^{2}-5ab + b^{2})-(-3a^{2}+2b^{2}+8ab)\) can be rewritten as \((3a^{2}-5ab + b^{2})+ (3a^{2}-2b^{2}-8ab)\). Grouping like - terms gives \((3a^{2}+3a^{2})+[-5ab+(-8ab)]+[b^{2}+(-2b^{2})]\).

Answer:

The additive inverse of the polynomial being subtracted is \(3a^{2}-2b^{2}-8ab\). The correct grouping of like - terms after rewriting subtraction as addition is \((3a^{2}+3a^{2})+[-5ab+(-8ab)]+[b^{2}+(-2b^{2})]\).