Question

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

Answer 1

The simplest form of
`X^2Y-Z` is
`3a^3-6a^2-2`

Option 2 is correct.

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`

Answer 2

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`