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The variables X, Y, and Z represent polynomials where X = a, Y = 3a – 5, and Z = a2 + 2. What is X2Y – Z in simplest form?


2a2 – 5a – 2

3a3 – 6a2 – 2

–3a3 – 2

–3a2 – 2

Verified Answer :

Answer : \(3a^3 - 6a^2 - 2\)

The variables X, Y, and Z represent polynomials where

X = a, Y = 3a – 5, and Z =  \(a^2 + 2\)

We need to find \(X^2Y - Z\)

We replace the values of X, Y and Z

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

Now we simplify it

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

isyllus

Answer:

The simplest form of \(X^2Y-Z\) is \(3a^3-6a^2-2\)

Option 2 is correct.

Step-by-step explanation:

Given: The variables X, Y, and Z represent polynomials.

\(X=a\)

\(Y=3a-5\)

\(Z=a^2+2\)

We need to find \(X^2Y-Z\)

Substitute the value of X, Y and Z into expression

\(\Rightarrow (a^2)(3a-5)-(a^2+2)\)

\(\Rightarrow 3a^3-5a^2-a^2-2\)

Combine the like term

\(\Rightarrow 3a^3-6a^2-2\)

Simplest form is \(\Rightarrow 3a^3-6a^2-2\)

Hence, The simplest form of \(X^2Y-Z\) is \(3a^3-6a^2-2\)

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