Question

Error analysis: Correct the error in finding the sum:

x - 4x + 3 + (-3x + 8x - 2) - (2x3 + 4x2 + 1)
Error: The sum of 3 and -2 is not 1.

Answer 1

To correct the error in finding the sum, simplify the given expression step by step by combining like terms and distributing the negative sign. The correct sum is 2x - 2 - 2x^3 - 4x^2 - 1.

Step-by-step explanation:

To correct the error in finding the sum, we need to simplify the given expression step by step:

x - 4x + 3 + (-3x + 8x - 2) - (2x3 + 4x2 + 1)

1. Combine like terms in each parenthesis: x - 4x + 3 + (-3x + 8x - 2) - (2x^3 + 4x^2 + 1) = x - 4x + 3 + -3x + 8x - 2 - 2x^3 - 4x^2 - 1
2. Combine like terms: -3x + 8x - 2 - 3x = 2x - 2 - 2x^3 - 4x^2 - 1
3. Combine like terms: 2x - 2 - 2x^3 - 4x^2 - 1 = (2x - 2) - (2x^3 + 4x^2 + 1)
4. Distribute the negative sign to the terms inside the second parenthesis: (2x - 2) - (2x^3 + 4x^2 + 1) = 2x - 2 - 2x^3 - 4x^2 - 1

After simplifying the expression, the correct sum is 2x - 2 - 2x^3 - 4x^2 - 1.

Answer 2

To correct the given error in finding the sum, we need to simplify the expression step by step by combining like terms and applying the proper rules of addition and subtraction.

Step-by-step explanation:

To correct the error in finding the sum, let's simplify the expression step by step:

1. Combine like terms within parentheses - (-3x + 8x) = 5x, (-4x + 3) = -x, and (2x^3 + 4x^2 + 1) remains the same. The expression becomes: x - 4x + 3 + 5x - x - (2x^3 + 4x^2 + 1)
2. Combine like terms outside the parentheses - x - 4x + 3 + 5x - x = x - 4x + 5x - x + 3 = x
3. Simplify the expression further - x - (2x^3 + 4x^2 + 1) = x - 2x^3 - 4x^2 - 1

Therefore, the corrected sum is x - 2x^3 - 4x^2 - 1.