1. $$ (x+9)(5) $$ $$ -4 x\left(x^{2}+8\right) $$ 3. $$ 2 a^{2}\left(5 b^{2}+3 a b+6 a+1\right) $$

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Simplify the expression by following steps:
- step0: Rearrange the terms:
  $$\left(x+9\right)\times 5$$
- step1: Multiply the terms:
  $$5\left(x+9\right)$$
- step2: Rearrange the terms:
  $$5x+45$$
Expand the expression $$ -4 x(x^{2}+8) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$-4x\left(x^{2}+8\right)$$
- step1: Apply the distributive property:
  $$-4x\times x^{2}-4x\times 8$$
- step2: Multiply the terms:
  $$-4x^{3}-32x$$
Expand the expression $$ 2 a^{2}(5 b^{2}+3 a b+6 a+1) $$
Simplify the expression by following steps:
- step0: Calculate:
  $$2a^{2}\left(5b^{2}+3ab+6a+1\right)$$
- step1: Rewrite the expression:
  $$2\left(5b^{2}+3ab+6a+1\right)a^{2}$$
- step2: Rearrange the terms:
  $$\left(5b^{2}+3ab+6a+1\right)\times 2a^{2}$$
- step3: Apply the distributive property:
  $$5b^{2}\times 2a^{2}+3ab\times 2a^{2}+6a\times 2a^{2}+1\times 2a^{2}$$
- step4: Multiply the numbers:
  $$10b^{2}a^{2}+6a^{3}b+12a^{3}+2a^{2}$$
Here are the expanded forms of the given expressions:

1. For $$ (x+9)(5) $$:
   $$
   5x + 45
   $$

2. For $$ -4 x(x^{2}+8) $$:
   $$
   -4x^{3} - 32x
   $$

3. For $$ 2 a^{2}(5 b^{2}+3 a b+6 a+1) $$:
   $$
   10b^{2}a^{2} + 6a^{3}b + 12a^{3} + 2a^{2}
   $$

If you have any further questions or need additional assistance, feel free to ask!
1. $$ 5x + 45 $$ 2. $$ -4x^{3} - 32x $$ 3. $$ 10a^{2}b^{2} + 6a^{3}b + 12a^{3} + 2a^{2} $$

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