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Answer :
Sure, let's simplify the given expression step-by-step:
The expression to simplify is:
[tex]\[ 14 x^5 \left( 13 x^2 + 13 x^5 \right) \][/tex]
Step 1: Distribute the factor [tex]\( 14 x^5 \)[/tex] to each term inside the parentheses.
This means we need to multiply [tex]\( 14 x^5 \)[/tex] by both [tex]\( 13 x^2 \)[/tex] and [tex]\( 13 x^5 \)[/tex]:
[tex]\[ 14 x^5 \cdot 13 x^2 + 14 x^5 \cdot 13 x^5 \][/tex]
Step 2: Multiply the coefficients and add the exponents for each term.
For the first term:
[tex]\[ 14 \cdot 13 \cdot x^{5+2} \][/tex]
[tex]\[ 14 \cdot 13 = 182 \][/tex]
[tex]\[ x^{5+2} = x^7 \][/tex]
So, the first term simplifies to:
[tex]\[ 182 x^7 \][/tex]
For the second term:
[tex]\[ 14 \cdot 13 \cdot x^{5+5} \][/tex]
[tex]\[ 14 \cdot 13 = 182 \][/tex]
[tex]\[ x^{5+5} = x^{10} \][/tex]
So, the second term simplifies to:
[tex]\[ 182 x^{10} \][/tex]
Step 3: Combine the simplified terms.
The final simplified expression is:
[tex]\[ 182 x^7 + 182 x^{10} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{182 x^7 + 182 x^{10}} \][/tex]
Looking at the provided multiple choices, the correct option is:
[tex]\[ \boxed{\text{c. } 182 x^7 + 182 x^{10}} \][/tex]
The expression to simplify is:
[tex]\[ 14 x^5 \left( 13 x^2 + 13 x^5 \right) \][/tex]
Step 1: Distribute the factor [tex]\( 14 x^5 \)[/tex] to each term inside the parentheses.
This means we need to multiply [tex]\( 14 x^5 \)[/tex] by both [tex]\( 13 x^2 \)[/tex] and [tex]\( 13 x^5 \)[/tex]:
[tex]\[ 14 x^5 \cdot 13 x^2 + 14 x^5 \cdot 13 x^5 \][/tex]
Step 2: Multiply the coefficients and add the exponents for each term.
For the first term:
[tex]\[ 14 \cdot 13 \cdot x^{5+2} \][/tex]
[tex]\[ 14 \cdot 13 = 182 \][/tex]
[tex]\[ x^{5+2} = x^7 \][/tex]
So, the first term simplifies to:
[tex]\[ 182 x^7 \][/tex]
For the second term:
[tex]\[ 14 \cdot 13 \cdot x^{5+5} \][/tex]
[tex]\[ 14 \cdot 13 = 182 \][/tex]
[tex]\[ x^{5+5} = x^{10} \][/tex]
So, the second term simplifies to:
[tex]\[ 182 x^{10} \][/tex]
Step 3: Combine the simplified terms.
The final simplified expression is:
[tex]\[ 182 x^7 + 182 x^{10} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{182 x^7 + 182 x^{10}} \][/tex]
Looking at the provided multiple choices, the correct option is:
[tex]\[ \boxed{\text{c. } 182 x^7 + 182 x^{10}} \][/tex]
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