Question

Докажите что значение выражения не зависит от значения переменной5х^3-5(x+2)(x^2-2x+4)

Answer 1

5х^3-5(х^3-2х^2+4х+2х^2-4х+8)==>сокращаем 4х и 2х^2=>5x^3-5x^3-40=-40

Answer 2

Expression Independence from Variable Value

To prove that the value of the expression does not depend on the value of the variable, we can simplify the expression and show that it does not contain the variable.

First, let's simplify the given expression step by step.

1. Expand the expression: The given expression is 5x^3 - 5(x+2)(x^2-2x+4).

2. Apply the distributive property: 5x^3 - 5(x^3 - 2x^2 + 4x + 2x^2 - 4x + 8).

3. Combine like terms: 5x^3 - 5x^3 + 10x^2 - 20x + 40.

4. Simplify: 10x^2 - 20x + 40.

Now, we can see that the simplified expression 10x^2 - 20x + 40 does not contain the variable x. Therefore, the value of the expression does not depend on the value of the variable x.

This proves that the given expression 5x^3 - 5(x+2)(x^2-2x+4) is independent of the value of the variable x.