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Answer :
Let's take a look at the given functions and simplify them to see if we can match them with any of the choices provided.
First, the functions given are:
1. [tex]\( f(x) = 16x^3 - 3x^3 \)[/tex]
2. [tex]\( y(x) = 7x^4 + 9x^3 \)[/tex]
### Step 1: Simplify [tex]\( f(x) \)[/tex]
[tex]\[
f(x) = 16x^3 - 3x^3 = 13x^3
\][/tex]
### Step 2: Observe [tex]\( y(x) \)[/tex]
The expression for [tex]\( y(x) \)[/tex] is already simplified:
[tex]\[
y(x) = 7x^4 + 9x^3
\][/tex]
### Matching with the given options:
Let's analyze each of the given options:
#### Option A:
[tex]\[ 77x^{11} + 99x^6 - 21x^6 + 27x^6 \][/tex]
This simplifies to:
[tex]\[ 77x^{11} + (99x^6 - 21x^6 + 27x^6) = 77x^{11} + 105x^6 \][/tex]
#### Option B:
[tex]\[ 18x^7 + 10x^6 + 6x^6 \][/tex]
This simplifies to:
[tex]\[ 18x^7 + (10x^6 + 6x^6) = 18x^7 + 16x^6 \][/tex]
#### Option G:
[tex]\[ 7x^4 + 99x^3 - 5x^2 \][/tex]
This is simply the expression itself. It doesn't simplify further.
#### The mention of "Heset" seems to be extraneous or a typo.
### Conclusion:
What we are looking for is a choice that could potentially equal either [tex]\( 13x^3 \)[/tex] or match one of the given functions more directly, possibly representing some kind of sum or operation we are missing from the context.
None of the given choices can exactly be derived directly from either [tex]\( f(x) \)[/tex] or [tex]\( y(x) \)[/tex] just by using addition or subtraction. They seem to involve different powers or terms than what [tex]\( f(x) \)[/tex] and [tex]\( y(x) \)[/tex] purely present after simplification.
The expressions given in the options either consist of much higher powers or do not directly correspond to any recognizable derivation from [tex]\( 13x^3 \)[/tex] or [tex]\( 7x^4 + 9x^3 \)[/tex]. Therefore, without additional context or operations defined, none of the given options appear to align with the simplified forms of [tex]\( f(x) \)[/tex] or [tex]\( y(x) \)[/tex].
Thus, based on the information you provided, we cannot determine a clear match. If there is additional context, you might want to refer to it for better insight into how these expressions should connect.
First, the functions given are:
1. [tex]\( f(x) = 16x^3 - 3x^3 \)[/tex]
2. [tex]\( y(x) = 7x^4 + 9x^3 \)[/tex]
### Step 1: Simplify [tex]\( f(x) \)[/tex]
[tex]\[
f(x) = 16x^3 - 3x^3 = 13x^3
\][/tex]
### Step 2: Observe [tex]\( y(x) \)[/tex]
The expression for [tex]\( y(x) \)[/tex] is already simplified:
[tex]\[
y(x) = 7x^4 + 9x^3
\][/tex]
### Matching with the given options:
Let's analyze each of the given options:
#### Option A:
[tex]\[ 77x^{11} + 99x^6 - 21x^6 + 27x^6 \][/tex]
This simplifies to:
[tex]\[ 77x^{11} + (99x^6 - 21x^6 + 27x^6) = 77x^{11} + 105x^6 \][/tex]
#### Option B:
[tex]\[ 18x^7 + 10x^6 + 6x^6 \][/tex]
This simplifies to:
[tex]\[ 18x^7 + (10x^6 + 6x^6) = 18x^7 + 16x^6 \][/tex]
#### Option G:
[tex]\[ 7x^4 + 99x^3 - 5x^2 \][/tex]
This is simply the expression itself. It doesn't simplify further.
#### The mention of "Heset" seems to be extraneous or a typo.
### Conclusion:
What we are looking for is a choice that could potentially equal either [tex]\( 13x^3 \)[/tex] or match one of the given functions more directly, possibly representing some kind of sum or operation we are missing from the context.
None of the given choices can exactly be derived directly from either [tex]\( f(x) \)[/tex] or [tex]\( y(x) \)[/tex] just by using addition or subtraction. They seem to involve different powers or terms than what [tex]\( f(x) \)[/tex] and [tex]\( y(x) \)[/tex] purely present after simplification.
The expressions given in the options either consist of much higher powers or do not directly correspond to any recognizable derivation from [tex]\( 13x^3 \)[/tex] or [tex]\( 7x^4 + 9x^3 \)[/tex]. Therefore, without additional context or operations defined, none of the given options appear to align with the simplified forms of [tex]\( f(x) \)[/tex] or [tex]\( y(x) \)[/tex].
Thus, based on the information you provided, we cannot determine a clear match. If there is additional context, you might want to refer to it for better insight into how these expressions should connect.
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