To simplify the expression \( 4x^2 (5x^3 + 4x + 1) - 9x^5 + 3x^2 + 4 \), we first distribute \( 4x^2 \) into the polynomial \( (5x^3 + 4x + 1) \):
\[ 4x^2 \cdot 5x^3 = 20x^5 \] \[ 4x^2 \cdot 4x = 16x^3 \] \[ 4x^2 \cdot 1 = 4x^2 \]
Now we combine these terms with the remaining parts of the expression:
\[ 20x^5 + 16x^3 + 4x^2 - 9x^5 + 3x^2 + 4 \]
Next, we combine like terms:
- For \(x^5\) terms: \(20x^5 - 9x^5 = 11x^5\)
- For \(x^3\) terms: \(16x^3\) (no other \(x^3\) term to combine)
- For \(x^2\) terms: \(4x^2 + 3x^2 = 7x^2\)
- The constant term is \(4\).
Putting it all together, the simplified expression is:
\[ 11x^5 + 16x^3 + 7x^2 + 4 \]
From this simplified expression, we identify the first and last terms:
- 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 \(11x^5\).
The last term is \(4\).