To simplify the expression \( 4x^2(5x^3 + 4x + 1) - 9x^5 + 3x^2 + 4 \), we start by distributing \( 4x^2 \) through the polynomial inside the parentheses.
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Distributing \( 4x^2 \): \[ 4x^2(5x^3) = 20x^5, \] \[ 4x^2(4x) = 16x^3, \] \[ 4x^2(1) = 4x^2. \]
Thus, \( 4x^2(5x^3 + 4x + 1) \) simplifies to: \[ 20x^5 + 16x^3 + 4x^2. \]
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Substitute back into the expression: \[ (20x^5 + 16x^3 + 4x^2) - 9x^5 + 3x^2 + 4. \]
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Combine like terms:
- For \( x^5 \): \[ 20x^5 - 9x^5 = 11x^5, \]
- For \( x^3 \): \[ 16x^3, \]
- For \( x^2 \): \[ 4x^2 + 3x^2 = 7x^2, \]
- The constant term is simply: \[ 4. \]
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Now, the expression is simplified to: \[ 11x^5 + 16x^3 + 7x^2 + 4. \]
From the simplified expression \( 11x^5 + 16x^3 + 7x^2 + 4 \), we can identify:
- The first term (the term with the highest degree) is \( 11x^5 \).
- The last term (the constant term) is \( 4 \).
Thus, the first term is \( 11x^5 \) and the last term is \( 4 \).