Math Problem Statement

Work out 4 × (1 + 2^2)^2

Solution

To solve the expression 4×(1+22)24 \times (1 + 2^2)^2, we follow the order of operations (BIDMAS/BODMAS):
Brackets → Indices → Division/Multiplication → Addition/Subtraction.


Step-by-Step Solution:

  1. Evaluate the power inside the brackets:
    22=42^2 = 4.

    Now the expression becomes:
    4×(1+4)24 \times (1 + 4)^2.

  2. Simplify inside the brackets:
    1+4=51 + 4 = 5.

    Now the expression becomes:
    4×524 \times 5^2.

  3. Calculate the square:
    52=255^2 = 25.

    Now the expression becomes:
    4×254 \times 25.

  4. Multiply:
    4×25=1004 \times 25 = 100.


Final Answer:

100100


Would you like further details on any of these steps? Let me know!

Related Questions:

  1. What is the order of operations in mathematics?
  2. How do you simplify expressions with powers and brackets?
  3. What happens if the order of operations is ignored?
  4. How do you expand (a+b)2(a + b)^2 algebraically?
  5. How do you simplify (3+22)2(3 + 2^2)^2?

Tip:

Always work inside the brackets first and then apply powers before multiplying or adding. This ensures the correct order of operations.

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Math Problem Analysis

Mathematical Concepts

Order of Operations (BIDMAS/BODMAS)
Exponents
Multiplication

Formulas

a^2 = a × a
Order of operations: Brackets → Indices → Division/Multiplication → Addition/Subtraction

Theorems

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Suitable Grade Level

Grades 6-8