Question

(a+3)(a^2-3a+9)-a(a-2)(a+2)​

Answer 1

Объяснение:

$(a+3)*(a^2-3a+9)-a*(a-2)*(a+2)=a^3+27-a*(a^2-4)=\\=a^3+27-a^3+4a=4a+27.$

Answer 2

To simplify the expression (a+3)(a^2-3a+9)-a(a-2)(a+2), you can start by expanding each part of the expression separately and then combining like terms. Here's the step-by-step simplification:

1. Expand the first term: (a+3)(a^2-3a+9)

   (a+3) * a^2 = a^3 + 3a^2 (a+3) * (-3a) = -3a^2 - 9a (a+3) * 9 = 9a + 27

   So, (a+3)(a^2-3a+9) = a^3 + 3a^2 - 3a^2 - 9a + 9a + 27

2. Now, expand the second term: a(a-2)(a+2)

   a * (a-2) = a^2 - 2a (a^2 - 2a) * (a+2) = a^3 + 2a^2 - 2a^2 - 4a

   So, a(a-2)(a+2) = a^3 - 4a

3. Now, you can simplify the original expression by subtracting the second term from the first term:

   (a^3 + 3a^2 - 3a^2 - 9a + 9a + 27) - (a^3 - 4a)

4. Simplify further:

   a^3 + 3a^2 - 3a^2 - 9a + 9a + 27 - a^3 + 4a

5. Now, combine like terms:

   (a^3 - a^3) + (3a^2 - 3a^2) + (-9a + 9a + 4a) + 27

6. The first two terms cancel out, and the third term simplifies to 0:

   0 + 0 + 0 + 27

7. The final simplified expression is:

   27

So, (a+3)(a^2-3a+9)-a(a-2)(a+2) simplifies to 27.