Let's evaluate each expression step by step.
1. Evaluate \( 5m+ 6n^2 - n^3 \) for \( m = 2 \) and \( n = 4 \)
Substituting the values of \( m \) and \( n \):
\[ 5m + 6n^2 - n^3 = 5(2) + 6(4^2) - (4^3) \]
Calculating each term:
- \( 5(2) = 10 \)
- \( 6(4^2) = 6 \times 16 = 96 \)
- \( 4^3 = 64 \)
Now substituting these values back into the expression:
\[ = 10 + 96 - 64 \] \[ = 10 + 96 = 106 \] \[ = 106 - 64 = 42 \]
So, the evaluated expression is:
\[ \textbf{42} \]
2. Evaluate \( (3x)^2 - (x^3 - y^2) \) for \( x = -3 \) and \( y = -5 \)
Substituting the values of \( x \) and \( y \):
\[ (3x)^2 - (x^3 - y^2) = (3(-3))^2 - ((-3)^3 - (-5)^2) \]
Calculating each part:
- \( 3(-3) = -9 \)
- \( (-9)^2 = 81 \)
- \( (-3)^3 = -27 \)
- \( (-5)^2 = 25 \)
Now substituting these values back into the expression:
\[ = 81 - (-27 - 25) \] \[ = 81 - (-27 - 25) = 81 - (-52) \] \[ = 81 + 52 = 133 \]
So, the evaluated expression is:
\[ \textbf{133} \]
Summary of Results
- The result of \( 5m + 6n^2 - n^3 \) is 42.
- The result of \( (3x)^2 - (x^3 - y^2) \) is 133.
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