The variables cap x , cap y , and cap z represent polynomials where cap x is equal to A , cap y is equal to 3 A minus 5 , and cap z is equal to A squared plus 2 What is cap x squared cap y minus cap z in simplest form?
Answer
A
2 A squared minus 5 A minus 2
B
3 A cubed minus 6 A squared minus 2
C
negative 3 A cubed minus 2
D
negative 3 A squared minus 2
Explanation
Substitute the expressions for the variables: x²y − z = A²(3A − 5) − (A² + 2). Distribute and combine like terms: 3A³ − 5A² − A² − 2 = 3A³ − 6A² − 2, which is choice B.
AI-written and checked against the verified answer.