Question

Помогите плиз! докажите, что значение выражения при всех а равно нулю! 1) (1+а)(1-а)(1+а^2)-1-а^4

Answer 1

= (1^2-a^2)(1+a^2)-(1-a^4)= (1^2-(a^2)^2) - (1 - a^4) = 1 - a^4 - 1 + a^4 = 0

Answer 2

Calculating the Expression

To prove that the expression is equal to zero, let's calculate the given expression step by step.

The given expression is: 1) (1 + a)(1 - a)(1 + a^2) - 1 - a^4

Let's simplify this expression step by step.

1. Expand the expression (1 + a)(1 - a)(1 + a^2): - (1 + a)(1 - a) = 1 - a^2 - (1 - a^2)(1 + a^2) = 1 - a^4

2. Substitute the result back into the original expression: - (1 - a^4) - 1 - a^4 = 1 - a^4 - 1 - a^4 = -2a^4

Conclusion

The given expression simplifies to -2a^4, which is not equal to zero for all values of 'a'. Therefore, the expression is not equal to zero for all values of 'a'.