Answer :
To simplify the expression [tex]\(14x^5(13x^2 + 13x^5)\)[/tex], we need to distribute [tex]\(14x^5\)[/tex] to each term inside the parentheses and then add the results:
1. Distribute [tex]\(14x^5\)[/tex] to [tex]\(13x^2\)[/tex]:
- First, multiply the coefficients: [tex]\(14 \times 13 = 182\)[/tex].
- Next, combine the powers of [tex]\(x\)[/tex]: [tex]\(x^5 \times x^2 = x^{5+2} = x^7\)[/tex].
- So, the first term becomes: [tex]\(182x^7\)[/tex].
2. Distribute [tex]\(14x^5\)[/tex] to [tex]\(13x^5\)[/tex]:
- Again, multiply the coefficients: [tex]\(14 \times 13 = 182\)[/tex].
- Combine the powers of [tex]\(x\)[/tex]: [tex]\(x^5 \times x^5 = x^{5+5} = x^{10}\)[/tex].
- So, the second term becomes: [tex]\(182x^{10}\)[/tex].
3. Combine the two terms:
- Add the terms together: [tex]\(182x^7 + 182x^{10}\)[/tex].
The fully simplified expression is [tex]\(182x^7 + 182x^{10}\)[/tex].
Therefore, the correct answer is option c: [tex]\(182x^7 + 182x^{10}\)[/tex].
1. Distribute [tex]\(14x^5\)[/tex] to [tex]\(13x^2\)[/tex]:
- First, multiply the coefficients: [tex]\(14 \times 13 = 182\)[/tex].
- Next, combine the powers of [tex]\(x\)[/tex]: [tex]\(x^5 \times x^2 = x^{5+2} = x^7\)[/tex].
- So, the first term becomes: [tex]\(182x^7\)[/tex].
2. Distribute [tex]\(14x^5\)[/tex] to [tex]\(13x^5\)[/tex]:
- Again, multiply the coefficients: [tex]\(14 \times 13 = 182\)[/tex].
- Combine the powers of [tex]\(x\)[/tex]: [tex]\(x^5 \times x^5 = x^{5+5} = x^{10}\)[/tex].
- So, the second term becomes: [tex]\(182x^{10}\)[/tex].
3. Combine the two terms:
- Add the terms together: [tex]\(182x^7 + 182x^{10}\)[/tex].
The fully simplified expression is [tex]\(182x^7 + 182x^{10}\)[/tex].
Therefore, the correct answer is option c: [tex]\(182x^7 + 182x^{10}\)[/tex].
