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Evaluate \[3 \times \left( {25 + \left[ {\left( { - 4} \right) \times \left( {16 - 2\, of\, 2} \right)} \right]} \right)\].

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Last updated date: 21st Feb 2024
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Answer
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Hint: We can solve this using the BODMAS rule. BODMAS is a short form for Brackets, of, Division, Multiplication, Addition and Subtraction. This rule explains the order of operations to solve an expression. According to the BODMAS rule in a given mathematical expression we must solve or simplify the brackets followed by division, multiplication addition and subtraction from left to right.

Complete step by step solution:
Given,
\[3 \times \left( {25 + \left[ {\left( { - 4} \right) \times \left( {16 - 2of2} \right)} \right]} \right)\]
We know that of means multiplication then
\[ = 3 \times \left( {25 + \left[ {\left( { - 4} \right) \times \left( {16 - \left( {2 \times 2} \right)} \right)} \right]} \right)\]
First follow the terms inside the brackets,
\[ = 3 \times \left( {25 + \left[ {\left( { - 4} \right) \times \left( {16 - 4} \right)} \right]} \right)\]
\[ = 3 \times \left( {25 + \left[ {\left( { - 4} \right) \times \left( {12} \right)} \right]} \right)\]
\[ = 3 \times \left( {25 + \left( { - 48} \right)} \right)\]
\[ = 3 \times \left( { - 23} \right)\]
\[ = - 69\]. This is the required answer.

Therefore, \[3 \times \left( {25 + \left[ {\left( { - 4} \right) \times \left( {16 - 2\,of\,2} \right)} \right]} \right) = -69 \].

Note:
In some regions the BODMAS rule is also known as PEDMAS. The PEDMAS means Parentheses, Exponents, Division, Multiplication, Addition and Subtraction. We also know that the product of two negative numbers results in a positive number. The product of a negative (positive) number and a positive (negative) number results in a negative number.