Answer :
To simplify the expression [tex]\(14x^5(13x^2 + 13x^5)\)[/tex], you need to use the distributive property. Here’s how you can do it step by step:
1. Distribute [tex]\(14x^5\)[/tex] to each term inside the parentheses:
- First, multiply [tex]\(14x^5\)[/tex] by [tex]\(13x^2\)[/tex]:
[tex]\[
14x^5 \times 13x^2 = (14 \times 13) \times x^{5+2} = 182x^7
\][/tex]
- Then, multiply [tex]\(14x^5\)[/tex] by [tex]\(13x^5\)[/tex]:
[tex]\[
14x^5 \times 13x^5 = (14 \times 13) \times x^{5+5} = 182x^{10}
\][/tex]
2. Combine the results:
The simplified expression after distributing is:
[tex]\[
182x^7 + 182x^{10}
\][/tex]
From the provided options, the correct choice is:
c. [tex]\(182x^7 + 182x^{10}\)[/tex]
This answer shows that we've distributed and combined the terms correctly using the rules of exponents and multiplication.
1. Distribute [tex]\(14x^5\)[/tex] to each term inside the parentheses:
- First, multiply [tex]\(14x^5\)[/tex] by [tex]\(13x^2\)[/tex]:
[tex]\[
14x^5 \times 13x^2 = (14 \times 13) \times x^{5+2} = 182x^7
\][/tex]
- Then, multiply [tex]\(14x^5\)[/tex] by [tex]\(13x^5\)[/tex]:
[tex]\[
14x^5 \times 13x^5 = (14 \times 13) \times x^{5+5} = 182x^{10}
\][/tex]
2. Combine the results:
The simplified expression after distributing is:
[tex]\[
182x^7 + 182x^{10}
\][/tex]
From the provided options, the correct choice is:
c. [tex]\(182x^7 + 182x^{10}\)[/tex]
This answer shows that we've distributed and combined the terms correctly using the rules of exponents and multiplication.
