To simplify the expression \( 4x^2(5x^3 + 4x + 1) - 9x^5 + 3x^2 + 4 \), we proceed with the following steps:
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Distribute \( 4x^2 \) across the terms in the parentheses: \[ 4x^2(5x^3) + 4x^2(4x) + 4x^2(1) = 20x^5 + 16x^3 + 4x^2 \]
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Incorporate the remaining terms in the original expression: \[ 20x^5 + 16x^3 + 4x^2 - 9x^5 + 3x^2 + 4 \]
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Combine like terms:
- For \( x^5 \) terms: \( 20x^5 - 9x^5 = 11x^5 \)
- For \( x^3 \) terms: Only \( 16x^3 \) is present.
- For \( x^2 \) terms: \( 4x^2 + 3x^2 = 7x^2 \)
- The constant term is \( 4 \).
Combining all these gives: \[ 11x^5 + 16x^3 + 7x^2 + 4 \]
The first term (the term with the highest degree) is \( 11x^5 \), and the last term (the constant term) is \( 4 \).
So, the final answer:
- First term: \( 11x^5 \)
- Last term: \( 4 \)
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