Multiply the expressions.

Question

x -- 25
x2-9

x -- 9x+18

x -- x-30

Select the correct choice below and fill in the answer box(es) within your choice.

OA.

x -- 9x+18
x2-x-30

O B.

x2-25
x2-9
(Simplify your answer. Use a comma to separate answers as needed.)

x2-9x+18
x -- x-30

x2-25
x2-9

and no numbers must be excluded.

Answer 1

To multiply the given expressions, let's first clarify them:

1. The first expression seems to be \( x - 25 \).
2. The second expression appears to be \( x^2 - 9 \).
3. The third expression is \( x - 9x + 18 \), which simplifies to \( -8x + 18 \).
4. The fourth expression is \( x - (x - 30) \), which simplifies to \( 30 \).

Now, let’s multiply the expressions:

1. First Pair: \( (x - 25)(x^2 - 9) \)

   • This is a difference of squares for \( x^2 - 9 \), which factors to \( (x - 3)(x + 3) \).
   • So the multiplication can be written as: \[ (x - 25)(x - 3)(x + 3) \]

2. Second Pair: \( (-8x + 18)(30) \)

   • This can be multiplied directly: \[ -8x \cdot 30 + 18 \cdot 30 = -240x + 540 \]

Now we can rewrite the combined multiplication as:

\[ (x - 25)(x^2 - 9) \cdot (-8x + 18) \cdot 30 \]

However, to provide the choice format that you listed (including the simplified versions), we can combine what we've calculated.

Given the choices:

Choice A:

• \( x - 9x + 18 \) simplifies to \( -8x + 18 \)
• \( x^2 - (x - 30) \) simplifies to \( x^2 - x + 30 \)

Choice B:

• \( x^2 - 25 \) is already factored.
• \( x^2 - 9 \) is also already factored.
• The product of these is \( (x - 5)(x + 5)(x - 3)(x + 3) \).

So the correct simplifications would be:

For \( OA \) be filled with:

• \( -8x + 18, , 30 \)

For \( OB \) choices:

• \( x^2 - 25, , x^2 - 9 \)

If you merely need the multiplications and simplifications, your selections would lead to:

• Choice A (simplified terms).
• Choice B (expressed in its polynomial factor forms).

Please clarify further if you need more in regards to operations or simplifications!