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].
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].
