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Simplify:

[tex]14 x^5\left(13 x^2+13 x^3\right)[/tex]

A. [tex]27 x^{10}+27 x^{20}[/tex]
B. [tex]182 x^{10}+13 x^3[/tex]
C. [tex]182 x^7+182 x^{10}[/tex]
D. [tex]27 x^7+27 x^{10}[/tex]

Answer :

Let's simplify the given expression step-by-step:

We are asked to simplify [tex]\( 14x^5(13x^2 + 13x^3) \)[/tex].

1. Distribute the terms inside the parentheses:

We apply the distributive property to multiply each term inside the parentheses by [tex]\( 14x^5 \)[/tex]:

[tex]\[
14x^5 \cdot 13x^2 + 14x^5 \cdot 13x^3
\][/tex]

2. Multiply each pair of terms:

- For the first term: [tex]\( 14x^5 \cdot 13x^2 = (14 \times 13) \cdot (x^5 \cdot x^2) = 182x^{5+2} = 182x^7 \)[/tex].

- For the second term: [tex]\( 14x^5 \cdot 13x^3 = (14 \times 13) \cdot (x^5 \cdot x^3) = 182x^{5+3} = 182x^8 \)[/tex].

3. Combine the results:

So after simplifying, the expression becomes:

[tex]\[
182x^7 + 182x^8
\][/tex]

Therefore, the simplified form of the expression is [tex]\( 182x^7 + 182x^8 \)[/tex].

This expression does not directly match any of the given options in the multiple-choice answers, which suggests there might be a mistake in the options provided. However, the correct simplified form is [tex]\( 182x^7 + 182x^8 \)[/tex].

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