Answer :
We start with the expression
[tex]$$14x^5\left(13x^2 + 13x^5\right).$$[/tex]
Step 1: Distribute the Term
Multiply [tex]$14x^5$[/tex] by each term inside the parentheses:
[tex]$$
14x^5 \cdot 13x^2 + 14x^5 \cdot 13x^5.
$$[/tex]
Step 2: Multiply the Coefficients
Multiply the constants for each term:
[tex]$$14 \cdot 13 = 182.$$[/tex]
Step 3: Multiply the Powers of [tex]\(x\)[/tex]
When multiplying powers of the same base, add the exponents:
- For the first term: [tex]$$x^5 \cdot x^2 = x^{5+2} = x^7.$$[/tex]
- For the second term: [tex]$$x^5 \cdot x^5 = x^{5+5} = x^{10}.$$[/tex]
Step 4: Write the Simplified Expression
Combine the results from the previous steps:
[tex]$$
182x^7 + 182x^{10}.
$$[/tex]
Comparing with the given choices, the correct option is:
c. [tex]\(182x^7 + 182x^{10}\)[/tex].
[tex]$$14x^5\left(13x^2 + 13x^5\right).$$[/tex]
Step 1: Distribute the Term
Multiply [tex]$14x^5$[/tex] by each term inside the parentheses:
[tex]$$
14x^5 \cdot 13x^2 + 14x^5 \cdot 13x^5.
$$[/tex]
Step 2: Multiply the Coefficients
Multiply the constants for each term:
[tex]$$14 \cdot 13 = 182.$$[/tex]
Step 3: Multiply the Powers of [tex]\(x\)[/tex]
When multiplying powers of the same base, add the exponents:
- For the first term: [tex]$$x^5 \cdot x^2 = x^{5+2} = x^7.$$[/tex]
- For the second term: [tex]$$x^5 \cdot x^5 = x^{5+5} = x^{10}.$$[/tex]
Step 4: Write the Simplified Expression
Combine the results from the previous steps:
[tex]$$
182x^7 + 182x^{10}.
$$[/tex]
Comparing with the given choices, the correct option is:
c. [tex]\(182x^7 + 182x^{10}\)[/tex].
