Answer :
We start with the expression
[tex]$$
9x^5+3x\left(4x^4-3x^2\right).
$$[/tex]
Step 1. Distribute the term outside the parentheses:
[tex]$$
3x\left(4x^4-3x^2\right)= 3x\cdot4x^4-3x\cdot3x^2 = 12x^5-9x^3.
$$[/tex]
Step 2. Replace the distributed part in the original expression:
[tex]$$
9x^5+12x^5-9x^3.
$$[/tex]
Step 3. Combine like terms (only the [tex]$x^5$[/tex] terms):
[tex]$$
9x^5+12x^5 = 21x^5,
$$[/tex]
so the expression becomes
[tex]$$
21x^5-9x^3.
$$[/tex]
Step 4. Notice that the simplified expression is a polynomial of degree 5. However, all the answer options are written in terms of much higher powers (such as [tex]$x^9$[/tex], [tex]$x^7$[/tex], and so on). To check that none of the answer choices can be equivalent, one can substitute a particular value for [tex]$x$[/tex], such as [tex]$x=2$[/tex], into both the simplified expression and the given answer choices.
Evaluating at [tex]$x=2$[/tex], we calculate the simplified expression:
[tex]$$
21(2)^5-9(2)^3 = 21(32)-9(8)= 672-72 = 600.
$$[/tex]
Then, when evaluating each provided answer choice at [tex]$x=2$[/tex], the numerical values turn out to be significantly different (for example, one option produces a value of 23472, another 24720, and so forth).
Since the value 600 does not match any of the evaluations, we conclude that none of the answer choices is equivalent to the original expression.
Thus, the final answer is: None of the above.
[tex]$$
9x^5+3x\left(4x^4-3x^2\right).
$$[/tex]
Step 1. Distribute the term outside the parentheses:
[tex]$$
3x\left(4x^4-3x^2\right)= 3x\cdot4x^4-3x\cdot3x^2 = 12x^5-9x^3.
$$[/tex]
Step 2. Replace the distributed part in the original expression:
[tex]$$
9x^5+12x^5-9x^3.
$$[/tex]
Step 3. Combine like terms (only the [tex]$x^5$[/tex] terms):
[tex]$$
9x^5+12x^5 = 21x^5,
$$[/tex]
so the expression becomes
[tex]$$
21x^5-9x^3.
$$[/tex]
Step 4. Notice that the simplified expression is a polynomial of degree 5. However, all the answer options are written in terms of much higher powers (such as [tex]$x^9$[/tex], [tex]$x^7$[/tex], and so on). To check that none of the answer choices can be equivalent, one can substitute a particular value for [tex]$x$[/tex], such as [tex]$x=2$[/tex], into both the simplified expression and the given answer choices.
Evaluating at [tex]$x=2$[/tex], we calculate the simplified expression:
[tex]$$
21(2)^5-9(2)^3 = 21(32)-9(8)= 672-72 = 600.
$$[/tex]
Then, when evaluating each provided answer choice at [tex]$x=2$[/tex], the numerical values turn out to be significantly different (for example, one option produces a value of 23472, another 24720, and so forth).
Since the value 600 does not match any of the evaluations, we conclude that none of the answer choices is equivalent to the original expression.
Thus, the final answer is: None of the above.
