Answer :
Sure, let's solve the problem step-by-step:
We need to perform the operation:
[tex]\[
(-9x^5 + 2x^7 - 2 - 4x^6) - (-6 - 9x^6 + 7x^7 - 2x^5)
\][/tex]
### Step 1: Distribute the negative sign
Subtracting a polynomial is the same as adding the opposite of each term inside it. Thus, we change the signs of each term in the second polynomial:
[tex]\[
- (-6 - 9x^6 + 7x^7 - 2x^5) = 6 + 9x^6 - 7x^7 + 2x^5
\][/tex]
### Step 2: Write the expression with distributed signs
Now, rewrite the expression with the distributed signs:
[tex]\[
(-9x^5 + 2x^7 - 2 - 4x^6) + (6 + 9x^6 - 7x^7 + 2x^5)
\][/tex]
### Step 3: Combine like terms
Next, we combine like terms:
- Combine the [tex]\(x^7\)[/tex] terms: [tex]\(2x^7 - 7x^7 = -5x^7\)[/tex]
- Combine the [tex]\(x^6\)[/tex] terms: [tex]\(-4x^6 + 9x^6 = 5x^6\)[/tex]
- Combine the [tex]\(x^5\)[/tex] terms: [tex]\(-9x^5 + 2x^5 = -7x^5\)[/tex]
- Combine the constant terms: [tex]\(-2 + 6 = 4\)[/tex]
### Final Expression
Putting it all together, we get:
[tex]\[
-5x^7 + 5x^6 - 7x^5 + 4
\][/tex]
So, the correct choice from the given options is:
[tex]\[
-5x^7 + 5x^6 - 7x^5 + 4
\][/tex]
We need to perform the operation:
[tex]\[
(-9x^5 + 2x^7 - 2 - 4x^6) - (-6 - 9x^6 + 7x^7 - 2x^5)
\][/tex]
### Step 1: Distribute the negative sign
Subtracting a polynomial is the same as adding the opposite of each term inside it. Thus, we change the signs of each term in the second polynomial:
[tex]\[
- (-6 - 9x^6 + 7x^7 - 2x^5) = 6 + 9x^6 - 7x^7 + 2x^5
\][/tex]
### Step 2: Write the expression with distributed signs
Now, rewrite the expression with the distributed signs:
[tex]\[
(-9x^5 + 2x^7 - 2 - 4x^6) + (6 + 9x^6 - 7x^7 + 2x^5)
\][/tex]
### Step 3: Combine like terms
Next, we combine like terms:
- Combine the [tex]\(x^7\)[/tex] terms: [tex]\(2x^7 - 7x^7 = -5x^7\)[/tex]
- Combine the [tex]\(x^6\)[/tex] terms: [tex]\(-4x^6 + 9x^6 = 5x^6\)[/tex]
- Combine the [tex]\(x^5\)[/tex] terms: [tex]\(-9x^5 + 2x^5 = -7x^5\)[/tex]
- Combine the constant terms: [tex]\(-2 + 6 = 4\)[/tex]
### Final Expression
Putting it all together, we get:
[tex]\[
-5x^7 + 5x^6 - 7x^5 + 4
\][/tex]
So, the correct choice from the given options is:
[tex]\[
-5x^7 + 5x^6 - 7x^5 + 4
\][/tex]
