Answer :
To solve the problem of finding the difference between the two given expressions, let's break it down step-by-step:
We are given two expressions:
1. [tex]\( 7x^9 + 9x^5 + 15 \)[/tex]
2. [tex]\( (10x^9 + 8x^5 + 12) \)[/tex]
We need to subtract the second expression from the first. This can be done by subtracting each corresponding term:
1. Subtract the [tex]\(x^9\)[/tex] terms:
[tex]\[
7x^9 - 10x^9 = (7 - 10)x^9 = -3x^9
\][/tex]
2. Subtract the [tex]\(x^5\)[/tex] terms:
[tex]\[
9x^5 - 8x^5 = (9 - 8)x^5 = 1x^5
\][/tex]
3. Subtract the constant terms:
[tex]\[
15 - 12 = 3
\][/tex]
Putting it all together, the expression after subtraction gives us:
[tex]\[
-3x^9 + 1x^5 + 3
\][/tex]
Looking at the multiple-choice options, the expression corresponds to option C:
[tex]\(-3x^9 + 17x^5 + 27\)[/tex].
Since none of the provided options correctly matches [tex]\(-3x^9 + 1x^5 + 3\)[/tex], it appears there is a mismatch in the options provided. However, based on our calculated difference, the correct simplified expression is [tex]\(-3x^9 + x^5 + 3\)[/tex].
We are given two expressions:
1. [tex]\( 7x^9 + 9x^5 + 15 \)[/tex]
2. [tex]\( (10x^9 + 8x^5 + 12) \)[/tex]
We need to subtract the second expression from the first. This can be done by subtracting each corresponding term:
1. Subtract the [tex]\(x^9\)[/tex] terms:
[tex]\[
7x^9 - 10x^9 = (7 - 10)x^9 = -3x^9
\][/tex]
2. Subtract the [tex]\(x^5\)[/tex] terms:
[tex]\[
9x^5 - 8x^5 = (9 - 8)x^5 = 1x^5
\][/tex]
3. Subtract the constant terms:
[tex]\[
15 - 12 = 3
\][/tex]
Putting it all together, the expression after subtraction gives us:
[tex]\[
-3x^9 + 1x^5 + 3
\][/tex]
Looking at the multiple-choice options, the expression corresponds to option C:
[tex]\(-3x^9 + 17x^5 + 27\)[/tex].
Since none of the provided options correctly matches [tex]\(-3x^9 + 1x^5 + 3\)[/tex], it appears there is a mismatch in the options provided. However, based on our calculated difference, the correct simplified expression is [tex]\(-3x^9 + x^5 + 3\)[/tex].
