the variables x, y, and z represent polynomials where x = a, y = 3a - 5, and z = a² + 2. what is x²y - z in…

Answer:

B. $3a^{3}-5a^{2}-2$

Explanation:

Step1: Calculate $X^{2}$

Since $X = a$, then $X^{2}=a\times a=a^{2}$.

Step2: Calculate $X^{2}Y$

$X^{2}Y=a^{2}(3a - 5)=3a^{3}-5a^{2}$ (using distributive property $m(n - p)=mn-mp$, here $m = a^{2}$, $n = 3a$, $p = 5$).

Step3: Calculate $X^{2}Y - Z$

$X^{2}Y - Z=(3a^{3}-5a^{2})-(a^{2}+2)=3a^{3}-5a^{2}-a^{2}-2=3a^{3}-6a^{2}-2$.