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Answer :
To find the difference between two polynomial expressions, you should subtract each corresponding term separately. Here's how you can do it step-by-step:
1. Write down the expressions:
The first expression is:
[tex]\( 21x^4 + 3x^2 - 7 \)[/tex]
The second expression is:
[tex]\( -5x^2 + 9x + 8 \)[/tex]
2. Set up the subtraction:
You want to subtract the second expression from the first:
[tex]\[
\left(21x^4 + 3x^2 - 7\right) - \left(-5x^2 + 9x + 8\right)
\][/tex]
3. Distribute the negative sign through the second expression:
[tex]\[
21x^4 + 3x^2 - 7 - (-5x^2) - 9x - 8
\][/tex]
Which simplifies to:
[tex]\[
21x^4 + 3x^2 - 7 + 5x^2 - 9x - 8
\][/tex]
4. Combine like terms:
- There is only one [tex]\( x^4 \)[/tex] term: [tex]\( 21x^4 \)[/tex]
- Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\( 3x^2 + 5x^2 = 8x^2 \)[/tex]
- The [tex]\( x \)[/tex] term is:
[tex]\(-9x\)[/tex]
- Combine the constant terms:
[tex]\(-7 - 8 = -15\)[/tex]
5. Write the resulting expression:
[tex]\[
21x^4 + 8x^2 - 9x - 15
\][/tex]
So, the difference between the polynomial expressions is:
[tex]\( 21x^4 + 8x^2 - 9x - 15 \)[/tex]
This matches the option:
[tex]\( 21x^4 + 8x^2 - 9x - 15 \)[/tex]
1. Write down the expressions:
The first expression is:
[tex]\( 21x^4 + 3x^2 - 7 \)[/tex]
The second expression is:
[tex]\( -5x^2 + 9x + 8 \)[/tex]
2. Set up the subtraction:
You want to subtract the second expression from the first:
[tex]\[
\left(21x^4 + 3x^2 - 7\right) - \left(-5x^2 + 9x + 8\right)
\][/tex]
3. Distribute the negative sign through the second expression:
[tex]\[
21x^4 + 3x^2 - 7 - (-5x^2) - 9x - 8
\][/tex]
Which simplifies to:
[tex]\[
21x^4 + 3x^2 - 7 + 5x^2 - 9x - 8
\][/tex]
4. Combine like terms:
- There is only one [tex]\( x^4 \)[/tex] term: [tex]\( 21x^4 \)[/tex]
- Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\( 3x^2 + 5x^2 = 8x^2 \)[/tex]
- The [tex]\( x \)[/tex] term is:
[tex]\(-9x\)[/tex]
- Combine the constant terms:
[tex]\(-7 - 8 = -15\)[/tex]
5. Write the resulting expression:
[tex]\[
21x^4 + 8x^2 - 9x - 15
\][/tex]
So, the difference between the polynomial expressions is:
[tex]\( 21x^4 + 8x^2 - 9x - 15 \)[/tex]
This matches the option:
[tex]\( 21x^4 + 8x^2 - 9x - 15 \)[/tex]
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