Question

А^9-9а^5-(а^4-9)(а^5+3)

Answer 1

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Answer 2

To simplify the expression $А^9 - 9а^5 - (а^4 - 9)(а^5 + 3)$, we can expand the second term within the parentheses and then combine like terms:

1. Expand the term inside the parentheses: $а^4 - 9$ can be written as $а^4 - 9 = (а^4 - 3^2)$ and $а^5 + 3$ can be written as $а^5 + 3 = (а^5 + 3)$.

2. Now, we can rewrite the expression as: $А^9 - 9а^5 - (а^4 - 9)(а^5 + 3) = А^9 - 9а^5 - (а^4 - 3^2)(а^5 + 3)$

3. Expand the term within the parentheses: $(а^4 - 3^2)(а^5 + 3) = а^4а^5 + 3а^4 - 3^2а^5 - 3^2$

4. Combine like terms: $а^4а^5$ and $-3^2а^5$ can be combined to $(а^4 - 3^2)а^5 = (а^4 - 9)а^5 = а^9$. $3а^4$ and $-3^2$ can be combined to $(3а^4 - 3^2) = 3(а^4 - 3) = 3(а^2 + 3)(а^2 - 3)$.

Now, our expression becomes: $А^9 - 9а^5 - (а^4 - 9)(а^5 + 3) = А^9 - 9а^5 - (а^9 + 3(а^2 + 3)(а^2 - 3))$

5. Distribute the negative sign: $А^9 - 9а^5 - (а^9 + 3(а^2 + 3)(а^2 - 3)) = А^9 - 9а^5 - а^9 - 3(а^2 + 3)(а^2 - 3)$

6. Combine like terms again: $А^9 - а^9$ cancels out, leaving us with: $- 9а^5 - 3(а^2 + 3)(а^2 - 3)$

7. Expand the remaining term $-3(а^2 + 3)(а^2 - 3)$: $-3(а^2 + 3)(а^2 - 3) = -3(а^4 - 9)$