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 complete 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) complete complete the statement. (3a² - 5ab + b²) - (-3a² + 2b² + 8ab) = 6a² - 13ab - b² 6a² - 3ab - 3b² -13ab - b²

Explanation:

Step1: Find additive inverse

The additive inverse of a polynomial $P(x)$ is $-P(x)$. Given the polynomial $-3a^{2}+2b^{2}+8ab$, its additive inverse is $-(-3a^{2}+2b^{2}+8ab)=3a^{2}-2b^{2}-8ab$.

Step2: Rewrite subtraction as addition

$(3a^{2}-5ab + b^{2})-(-3a^{2}+2b^{2}+8ab)=(3a^{2}-5ab + b^{2})+(3a^{2}-2b^{2}-8ab)$.

Step3: Group like - terms

Group the $a^{2}$ terms: $3a^{2}+3a^{2}$, the $ab$ terms: $-5ab+( - 8ab)$, and the $b^{2}$ terms: $b^{2}+(-2b^{2})$, so we have $(3a^{2}+3a^{2})+[-5ab+( - 8ab)]+[b^{2}+(-2b^{2})]$.

Step4: Simplify the polynomial

$(3a^{2}+3a^{2})+[-5ab+( - 8ab)]+[b^{2}+(-2b^{2})]=6a^{2}-13ab - b^{2}$.

Answer:

Additive inverse: $3a^{2}-2b^{2}-8ab$
Grouping of like - terms: $(3a^{2}+3a^{2})+[-5ab+( - 8ab)]+[b^{2}+(-2b^{2})]$
Simplified result: $6a^{2}-13ab - b^{2}$