Question
Multiply the expressions.
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.
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.
Answers
GPT-4o mini
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!
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!