Question

Докажите что значение выражения 6(9х^3+2)-2(1-3х+9х^2)(1+3х) не зависит от значения переменной

Answer 1

...=54х^3+12-2(1-3х+9х^2+3х-9х^2+27х^3)=54х^3+12-2-54х^3=10
Там все слагаемые с х самоуничтожаются (одинаковые слагаемые с разными знаками)
Вот и всё доказательство

Answer 2

Proving the Expression's Independence from the Variable Value

To prove that the expression 6(9x^3+2)-2(1-3x+9x^2)(1+3x) does not depend on the value of the variable x, we can simplify the expression and show that the variable x does not affect the result.

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

1. Expand the terms inside the parentheses. 2. Combine like terms. 3. Factor out common terms.

Simplifying the Expression

The given expression is: 6(9x^3+2)-2(1-3x+9x^2)(1+3x)

Expanding the terms inside the parentheses: 6 * 9x^3 + 6 * 2 - 2 * (1 * 1 + 1 * 3x - 3x * 1 - 3x * 3x + 9x^2 * 1 + 9x^2 * 3x)

Simplifying further: 54x^3 + 12 - 2(1 + 3x - 3x - 9x^2 + 9x^2 + 27x^3)

Combining like terms: 54x^3 + 12 - 2(1 + 27x^3)

Further simplification: 54x^3 + 12 - 2 - 54x^3

Final Simplified Expression

The final simplified expression is: 12 - 2

Conclusion

As we can see, the variable x does not appear in the final simplified expression. Therefore, the value of the expression 6(9x^3+2)-2(1-3x+9x^2)(1+3x) does not depend on the value of the variable x.

The expression 6(9x^3+2)-2(1-3x+9x^2)(1+3x) is independent of the value of the variable x.