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Answer :
Certainly! Let's simplify the expression step-by-step:
Given the expression:
[tex]\[
(7x^2 - 5x^6 + 7) + (9x^6 - 3 + 7x^2)
\][/tex]
1. Identify and Group Like Terms:
- Both expressions have terms with [tex]\(x^6\)[/tex], [tex]\(x^2\)[/tex], and constant terms. So, we'll group these:
- [tex]\(x^6\)[/tex] terms: [tex]\(-5x^6\)[/tex] and [tex]\(9x^6\)[/tex]
- [tex]\(x^2\)[/tex] terms: [tex]\(7x^2\)[/tex] and [tex]\(7x^2\)[/tex]
- Constant terms: [tex]\(7\)[/tex] and [tex]\(-3\)[/tex]
2. Combine Like Terms:
- Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
-5x^6 + 9x^6 = 4x^6
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
7x^2 + 7x^2 = 14x^2
\][/tex]
- Combine the constant terms:
[tex]\[
7 - 3 = 4
\][/tex]
3. Write the Simplified Expression:
- After combining the like terms, the expression simplifies to:
[tex]\[
4x^6 + 14x^2 + 4
\][/tex]
So, the simplified expression is [tex]\(4x^6 + 14x^2 + 4\)[/tex].
Given the expression:
[tex]\[
(7x^2 - 5x^6 + 7) + (9x^6 - 3 + 7x^2)
\][/tex]
1. Identify and Group Like Terms:
- Both expressions have terms with [tex]\(x^6\)[/tex], [tex]\(x^2\)[/tex], and constant terms. So, we'll group these:
- [tex]\(x^6\)[/tex] terms: [tex]\(-5x^6\)[/tex] and [tex]\(9x^6\)[/tex]
- [tex]\(x^2\)[/tex] terms: [tex]\(7x^2\)[/tex] and [tex]\(7x^2\)[/tex]
- Constant terms: [tex]\(7\)[/tex] and [tex]\(-3\)[/tex]
2. Combine Like Terms:
- Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
-5x^6 + 9x^6 = 4x^6
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
7x^2 + 7x^2 = 14x^2
\][/tex]
- Combine the constant terms:
[tex]\[
7 - 3 = 4
\][/tex]
3. Write the Simplified Expression:
- After combining the like terms, the expression simplifies to:
[tex]\[
4x^6 + 14x^2 + 4
\][/tex]
So, the simplified expression is [tex]\(4x^6 + 14x^2 + 4\)[/tex].
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