Question

simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)
options:
5b⁴ - 2b³ + 7
4b⁴ - 2b³ + 7
5b⁴ - 2b³ + 4
b⁴ - 2b³ + 7

Explanation:

Step1: Distribute the negative sign

$(6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2) = 6b^3 + 6 - b^4 - 8b^3 + 6b^4 - 2$

Step2: Combine like $b^4$ terms

$-b^4 + 6b^4 = 5b^4$

Step3: Combine like $b^3$ terms

$6b^3 - 8b^3 = -2b^3$

Step4: Combine constant terms

$6 - 2 = 4$

Step5: Combine all simplified terms

$5b^4 - 2b^3 + 4$

Answer:

$5b^4 - 2b^3 + 4$