Answer :
To simplify the expression [tex]\(6x^6 + 9x^7 + 2x^6 + 5 + 7x^7\)[/tex], you need to combine like terms. Here are the steps:
1. Identify Like Terms: Look for terms with the same variable raised to the same power.
- The terms [tex]\(6x^6\)[/tex] and [tex]\(2x^6\)[/tex] are like terms because both involve [tex]\(x^6\)[/tex].
- The terms [tex]\(9x^7\)[/tex] and [tex]\(7x^7\)[/tex] are like terms because both involve [tex]\(x^7\)[/tex].
- The number [tex]\(5\)[/tex] is a constant term and does not combine with terms involving [tex]\(x\)[/tex].
2. Combine Like Terms:
- Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
6x^6 + 2x^6 = 8x^6
\][/tex]
- Combine the [tex]\(x^7\)[/tex] terms:
[tex]\[
9x^7 + 7x^7 = 16x^7
\][/tex]
3. Write the Simplified Expression:
Put all the terms together after combining:
[tex]\[
8x^6 + 16x^7 + 5
\][/tex]
So, the simplified expression is [tex]\(8x^6 + 16x^7 + 5\)[/tex].
1. Identify Like Terms: Look for terms with the same variable raised to the same power.
- The terms [tex]\(6x^6\)[/tex] and [tex]\(2x^6\)[/tex] are like terms because both involve [tex]\(x^6\)[/tex].
- The terms [tex]\(9x^7\)[/tex] and [tex]\(7x^7\)[/tex] are like terms because both involve [tex]\(x^7\)[/tex].
- The number [tex]\(5\)[/tex] is a constant term and does not combine with terms involving [tex]\(x\)[/tex].
2. Combine Like Terms:
- Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
6x^6 + 2x^6 = 8x^6
\][/tex]
- Combine the [tex]\(x^7\)[/tex] terms:
[tex]\[
9x^7 + 7x^7 = 16x^7
\][/tex]
3. Write the Simplified Expression:
Put all the terms together after combining:
[tex]\[
8x^6 + 16x^7 + 5
\][/tex]
So, the simplified expression is [tex]\(8x^6 + 16x^7 + 5\)[/tex].
