Detailed Mathematical Analysis

Analysis of Mathematical Expressions

Breakdown of Expressions

Expression 1: (5-10-14(2-0))
  • This expression appears to include a combination of arithmetic operations. First, we identify the operation within the parentheses:
      - Simplification of the inner part: The operation is (2 - 0), which simplifies to 2.
      - The outer expression now looks like: (5 - 10 - 14(2)).
Consecutive Subtractions and Multiplication
  • Moving to the next operations, we sequentially calculate:
      - Calculate 14 multiplied by 2 which is 14imes2=2814 imes 2 = 28
  • Now, the expression can be rewritten as:
      - 5−10−285 - 10 - 28
      - Continuing the arithmetic gives:
        - First handle the subtractions: 5−10=−55 - 10 = -5
        - Then, −5−28=−33-5 - 28 = -33
  • Hence, the final evaluated result of this expression is -33.
Expression 2: £ (= -1)+(y)
  • This notation is somewhat ambiguous but typically represents financial money (pound sterling). The statement seems to suggest an equation or a balance.
      - If interpreted as an equation: £ (which we assume to represent a variable or amount of currency) is equal to -1 plus y.
      - Hence, we can express it mathematically as:
        - £=−1+y£ = -1 + y
        - This indicates a relationship or condition where variable £ is influenced by some quantity y.
Expression 3: (x-2)(53)
  • Here, we have factors involving a variable x. This can be expressed as:
      - 53imes(x−2)53 imes (x - 2)
  • This indicates that the expression will evaluate differently based on the value consumed by x. To expand, we can apply distributive property:
      - 53x−10653x - 106
Expression 4: (-24 + 86)
  • This segment is straightforward. Performing the addition:
      - Sum yields: −24+86=62-24 + 86 = 62
Expression 5: -8x(3x-1)
  • Here we have a product of terms involving the variable x. First, expand the expression:
      - Using distributive property:
        - −8x(3x−1)=−8ximes3x+8x-8x (3x-1) = -8x imes 3x + 8x
        - This simplifies to: −24x2+8x-24x^2 + 8x
Expression 6: 16
  • This number appears as a standalone expression, presumably as a constant highlighting its value of 16.
Expression 7: a(64)
  • This expression signifies multiplication where a variable a is being multiplied by 64. Thus, it can be expressed as:
      - 64a64a

Summary of Evaluated Results

  • The detailed calculations yield:
      - Expression 1 results in -33.
      - Expression 2 is expressed as £=−1+y£ = -1 + y.
      - Expression 3 simplifies to 53x−10653x - 106.
      - Expression 4 yields 62.
      - Expression 5 simplifies to −24x2+8x-24x^2 + 8x.
      - Expression 6 identifies the value as 16.
      - Expression 7 represents 64a.