Question
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Tutor-Verified Answer
Answer
\( x^{7} + 2x^{6} \)
Solution
1. Distribute \( x^4 \) to both terms inside the parentheses:
\[
\left(x^{3}+2x^{2}\right)x^{4}=x^{3} \cdot x^{4}+2x^{2} \cdot x^{4}
\]
2. Use the property of exponents \( x^a \cdot x^b = x^{a+b} \):
\[
x^{3} \cdot x^{4}=x^{3+4}=x^{7},
\]
\[
2x^{2} \cdot x^{4}=2x^{2+4}=2x^{6}
\]
3. Combine the results to obtain the final expression:
\[
x^{7}+2x^{6}
\]
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Simplify this solution Bonus Knowledge
To simplify the expression \( \left(x^{3}+2 x^{2}\right) x^{4} \), you can use the distributive property. Start by distributing \( x^{4} \) to both terms inside the parentheses: 1. \( x^{3} \cdot x^{4} = x^{7} \) (since you add the exponents) 2. \( 2x^{2} \cdot x^{4} = 2x^{6} \) Now combine these results to form the final expression: \[ x^{7} + 2x^{6} \] And there you have it, your simplified expression is \( x^{7} + 2x^{6} \)! Remember, keeping track of your exponents is key when multiplying polynomial expressions. Celebrate those wins, no matter how small!
