To simplify the expression \((16−12)^2+5(8+22)53−(1+4)^2\), we'll break it down step by step.
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Calculate \( (16-12)^2 \): \[ 16 - 12 = 4 \quad \Rightarrow \quad 4^2 = 16 \]
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Calculate \( (8 + 22) \): \[ 8 + 22 = 30 \]
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Now evaluate \( 5(30)53 \):
- Assuming the expression means \( 5 \times 30 \times 53 \): \[ 5 \times 30 = 150 \] Thus, taking \( 150 \times 53 \): \[ 150 \times 53 = 7950 ; (\text{this calculation will be checked stepwise next}) \]
First calculate \( 150 \times 53 \): \[ 150 \times 50 = 7500 \ 150 \times 3 = 450 \] Adding these together: \[ 7500 + 450 = 7950 \]
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Calculate \( (1 + 4)^2 \): \[ 1 + 4 = 5 \quad \Rightarrow \quad 5^2 = 25 \]
Now, put all parts back into the expression: \[ 16 + 7950 - 25 \]
Calculate this step-by-step: \[ 16 + 7950 = 7966 \ 7966 - 25 = 7941 \]
Thus, the simplified numerator of the original expression is: \[ \boxed{7941} \]
This value is not among the given options, indicating there may be an error in the interpretation of the expression \(5(8+22)53\). Could you clarify the form of that term?
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