To evaluate the expression \( 4y^3 - 17 + 9y^2 + \left( \frac{24}{3} \right) \) when \( y = 3 \), follow these steps:
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Substitute \( y = 3 \) into the expression: \[ 4(3)^3 - 17 + 9(3)^2 + \left( \frac{24}{3} \right) \]
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Calculate \( 3^3 \) and \( 3^2 \): \[ 3^3 = 27 \quad \text{and} \quad 3^2 = 9 \]
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Substitute these values back into the expression: \[ 4(27) - 17 + 9(9) + 8 \]
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Calculate each term: \[ 4 \times 27 = 108 \] \[ 9 \times 9 = 81 \]
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Now write the entire expression with the calculated values: \[ 108 - 17 + 81 + 8 \]
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Simplify the expression step by step: \[ 108 - 17 = 91 \] \[ 91 + 81 = 172 \] \[ 172 + 8 = 180 \]
Thus, the value of the expression when \( y = 3 \) is \( \boxed{180} \).
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