Answer :
To simplify the expression [tex]\(4x^5 - 6x^6 + 2x^5 - 7x^5\)[/tex], we'll follow these steps:
1. Combine Like Terms:
- First, identify terms with the same power of [tex]\(x\)[/tex].
- The terms [tex]\(4x^5\)[/tex], [tex]\(2x^5\)[/tex], and [tex]\(-7x^5\)[/tex] are all like terms because they each have [tex]\(x^5\)[/tex].
2. Add/Subtract the Coefficients of Like Terms:
- Combine the coefficients of [tex]\(x^5\)[/tex]:
[tex]\[
4x^5 + 2x^5 - 7x^5 = (4 + 2 - 7)x^5 = -1x^5 \text{ or simply } -x^5
\][/tex]
3. Consider Remaining Terms:
- The term [tex]\(-6x^6\)[/tex] doesn't combine with anything else because it's the only [tex]\(x^6\)[/tex] term.
4. Write the Simplified Expression:
- Combine the results from steps 2 and 3 to get:
[tex]\[
-6x^6 - x^5
\][/tex]
5. Factor the Expression (Optional):
- If you want to factor the expression, you can factor out [tex]\(-x^5\)[/tex] from both terms:
[tex]\[
-x^5(6x + 1)
\][/tex]
So, the simplified expression is:
[tex]\[
-x^5(6x + 1)
\][/tex]
This is the final form of the given expression after simplification.
1. Combine Like Terms:
- First, identify terms with the same power of [tex]\(x\)[/tex].
- The terms [tex]\(4x^5\)[/tex], [tex]\(2x^5\)[/tex], and [tex]\(-7x^5\)[/tex] are all like terms because they each have [tex]\(x^5\)[/tex].
2. Add/Subtract the Coefficients of Like Terms:
- Combine the coefficients of [tex]\(x^5\)[/tex]:
[tex]\[
4x^5 + 2x^5 - 7x^5 = (4 + 2 - 7)x^5 = -1x^5 \text{ or simply } -x^5
\][/tex]
3. Consider Remaining Terms:
- The term [tex]\(-6x^6\)[/tex] doesn't combine with anything else because it's the only [tex]\(x^6\)[/tex] term.
4. Write the Simplified Expression:
- Combine the results from steps 2 and 3 to get:
[tex]\[
-6x^6 - x^5
\][/tex]
5. Factor the Expression (Optional):
- If you want to factor the expression, you can factor out [tex]\(-x^5\)[/tex] from both terms:
[tex]\[
-x^5(6x + 1)
\][/tex]
So, the simplified expression is:
[tex]\[
-x^5(6x + 1)
\][/tex]
This is the final form of the given expression after simplification.
