College

Simplify

[tex] \[ 14 x^5\left(13 x^2+13 x^5\right) \] [/tex]

A. [tex] \[ 27 x^{10}+27 x^{25} \] [/tex]

B. [tex] \[ 182 x^{10}+13 x^5 \] [/tex]

C. [tex] \[ 182 x^7+182 x^{10} \] [/tex]

D. [tex] \[ 27 x^7+27 x^{10} \] [/tex]

Answer :

Sure! Let's simplify the expression step-by-step:

We have the expression [tex]\(14x^5(13x^2 + 13x^5)\)[/tex].

1. Use the Distributive Property:
- Distribute [tex]\(14x^5\)[/tex] to each term inside the parentheses.

2. First Term:
- Multiply [tex]\(14x^5\)[/tex] by [tex]\(13x^2\)[/tex].
- [tex]\(14 \times 13 = 182\)[/tex]
- [tex]\(x^5 \times x^2 = x^{5+2} = x^7\)[/tex]
- Combine these to get [tex]\(182x^7\)[/tex].

3. Second Term:
- Multiply [tex]\(14x^5\)[/tex] by [tex]\(13x^5\)[/tex].
- [tex]\(14 \times 13 = 182\)[/tex]
- [tex]\(x^5 \times x^5 = x^{5+5} = x^{10}\)[/tex]
- Combine these to get [tex]\(182x^{10}\)[/tex].

4. Combine the Terms:
- The simplified expression is [tex]\(182x^7 + 182x^{10}\)[/tex].

So, the correct answer is c. [tex]\(182x^7 + 182x^{10}\)[/tex].

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