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The variables X, Y, and Z represent polynomials where X = a, Y = 3a – 5, and Z = a^2 + 2. What is X^2Y – Z in simplest form?

A2a^2 – 5a – 2
B3a^3 – 6a^2 – 2
C–3a^3 – 2
D–3a^2 – 2

Verified Answer :

naǫ

\(X=a \\ Y=3a-5 \\ Z=a^2+2 \\ \\ X^2Y-Z=a^2(3a-5)-(a^2+2)=3a^3-5a^2-a^2-2=3a^3-6a^2-2\)

The answer is b.

Answer:  Option 'b' is correct.

Step-by-step explanation:

Since we have given that

\(X=a\\\\Y=3a-5\\\\Z=a^2+2\)

We need to calculate :

\(X^2Y-Z\)

So, we put the values of X, Y, and Z in the expression, then it becomes,

\(X^2Y-Z=a^2(3a-5)-(a^2+2)\\\\X^2Y-Z=3a^3-5a^2-a^2-2\\\\X^2Y-Z=3a^3-6a^2-2\)

Hence, Option 'b' is correct.

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