Polynomial Operations — Test

Question 16 • Algebra II

What is the product? open paren negative 6 A cubed b plus 2 A b squared close paren times open paren 5 A squared minus 2 A b squared minus b close paren

Answer

30 A to the 6th power b minus 12 A cubed b squared minus 6 A cubed b plus 10 A squared b squared minus 4 A b to the 4th power minus 2 A b squared

negative 30 A to the 5th power b plus 12 A to the 4th power b cubed plus 16 A cubed b squared minus 4 A squared b to the 4th power minus 2 A b cubed

30 A to the 5th power b minus 12 A to the 4th power b cubed plus 4 A cubed b squared minus 4 A squared b to the 4th power minus 2 A b cubed

negative 30 A to the 6th power b plus 12 A cubed b squared plus 6 A cubed b plus 10 A squared b squared minus 4 A b to the 4th power minus 2 A b squared

Explanation

Distribute each term in the first parentheses across the second. The products are −30A⁵b, 12A⁴b³, 6A³b², 10A³b², −4A²b⁴, and −2Ab³. Combine the like terms 6A³b² and 10A³b² to get 16A³b². The result matches choice B: −30A⁵b + 12A⁴b³ + 16A³b² − 4A²b⁴ − 2Ab³.

AI-written and checked against the verified answer.

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