Question

Докажите что значение выражения (p-3)(p^2+3p+9)-p^3 не зависит от значения p

Answer 1

Решение смотри на фотографии

Answer 2

(p-3)(p²+3p+9)-p³=p³-27-p³=-27

-27 не зависит от значения p

Answer 3

Understanding the Expression

The given expression is (p-3)(p^2+3p+9)-p^3. We need to prove that the value of this expression does not depend on the value of p.

Proof

Let's expand the given expression and simplify it to see if the value depends on the variable p.

Expanding the expression: (p-3)(p^2+3p+9)-p^3

Simplify the first part: (p-3)(p^2+3p+9) = p(p^2+3p+9) - 3(p^2+3p+9)

Now, expand and simplify further: = p^3 + 3p^2 + 9p - 3p^2 - 9p - 27 - p^3

Simplify the expression: = -27

Conclusion

The value of the given expression (p-3)(p^2+3p+9)-p^3 simplifies to -27 regardless of the value of p. Therefore, the value of the expression does not depend on the value of p.