Question

muiltiply the polynomial expression (x+2)*(x-4)

Answer 1

There needs to be a number before the first x

Answer 2

Multiply to simplify the polynomial expression (r-1)*(r^2-2r+3)

Answer 3

simplify the polynomial expression (xy-2)*(x^2+1)

Answer 4

Multiply the polynomial (b+8)*3b-6)

Answer 5

what is a product of the polynomials (x^2y+2)(x^2-y)

Answer 6

To multiply the polynomial expressions \((x + 2)(x - 4)\), you can use the distributive property (also known as the FOIL method for binomials). Here's how it works step-by-step:

1. **First:** Multiply the first terms:
\(x \cdot x = x^2\)

2. **Outer:** Multiply the outer terms:
\(x \cdot (-4) = -4x\)

3. **Inner:** Multiply the inner terms:
\(2 \cdot x = 2x\)

4. **Last:** Multiply the last terms:
\(2 \cdot (-4) = -8\)

Now, combine all these results:

\[
x^2 - 4x + 2x - 8
\]

Combine like terms:

\[
x^2 - 2x - 8
\]

So, the product of the polynomial expression \((x + 2)(x - 4)\) is:

\[
\boxed{x^2 - 2x - 8}
\]

Answer 7

It appears there might be a misunderstanding regarding the polynomial expression.

The multiplication of the polynomials you provided, \((x + 2)(x - 4)\), results in:

\[
x^2 - 2x - 8
\]

If you want the polynomial in a different form or if you meant to include a number coefficient in front of the \(x\), please clarify. For instance, you can multiply the entire expression by a number. For example, if you wanted the expression to have a coefficient of, say, 3 in front of \(x\), you would write it as:

\[
3(x + 2)(x - 4)
\]

If you meant something different, please provide more details so I can assist you accurately!

Answer 8

To multiply and simplify the polynomial expression \( (r - 1)(r^2 - 2r + 3) \), use the distributive property (or FOIL). Here’s the step-by-step process:

1. **Distribute \( r \) to each term in \( r^2 - 2r + 3 \)**:
\[
r \cdot r^2 = r^3
\]
\[
r \cdot (-2r) = -2r^2
\]
\[
r \cdot 3 = 3r
\]

2. **Distribute \( -1 \) to each term in \( r^2 - 2r + 3 \)**:
\[
-1 \cdot r^2 = -r^2
\]
\[
-1 \cdot (-2r) = 2r
\]
\[
-1 \cdot 3 = -3
\]

Now, combine all the results:

\[
r^3 - 2r^2 + 3r - r^2 + 2r - 3
\]

Next, combine like terms:

- The \( r^2 \) terms: \( -2r^2 - r^2 = -3r^2 \)
- The \( r \) terms: \( 3r + 2r = 5r \)

Putting it all together, the expression simplifies to:

\[
r^3 - 3r^2 + 5r - 3
\]

Thus, the simplified form of the polynomial expression \( (r - 1)(r^2 - 2r + 3) \) is:

\[
\boxed{r^3 - 3r^2 + 5r - 3}
\]

Answer 9

To simplify the polynomial expression \((xy - 2)(x^2 + 1)\), we can use the distributive property. Here's how to do it step by step:

1. **Distribute \(xy\) to each term in \(x^2 + 1\)**:
\[
xy \cdot x^2 = xyx^2 = x^3y
\]
\[
xy \cdot 1 = xy
\]

2. **Distribute \(-2\) to each term in \(x^2 + 1\)**:
\[
-2 \cdot x^2 = -2x^2
\]
\[
-2 \cdot 1 = -2
\]

Now, combine all the results:

\[
x^3y + xy - 2x^2 - 2
\]

Now, we organize the terms:

The final expression is:

\[
\boxed{x^3y - 2x^2 + xy - 2}
\]

This is the simplified form of the polynomial expression \((xy - 2)(x^2 + 1)\).

Answer 10

To multiply the polynomial expression \( (b + 8)(3b - 6) \), we'll use the distributive property (or FOIL method). Here’s how to do it step by step:

1. **Distribute \( b \) to each term in \( (3b - 6) \)**:
\[
b \cdot 3b = 3b^2
\]
\[
b \cdot (-6) = -6b
\]

2. **Distribute \( 8 \) to each term in \( (3b - 6) \)**:
\[
8 \cdot 3b = 24b
\]
\[
8 \cdot (-6) = -48
\]

Now, combine all these results:

\[
3b^2 - 6b + 24b - 48
\]

Next, combine like terms:

- The \( b \) terms: \( -6b + 24b = 18b \)

Putting it all together, the expression simplifies to:

\[
3b^2 + 18b - 48
\]

Therefore, the product of the polynomial expression \( (b + 8)(3b - 6) \) is:

\[
\boxed{3b^2 + 18b - 48}
\]

Answer 11

To multiply the polynomials \((x^2y + 2)(x^2 - y)\), we can use the distributive property. Here’s how to do it step by step:

1. **Distribute \(x^2y\) to each term in \((x^2 - y)\)**:
\[
x^2y \cdot x^2 = x^4y
\]
\[
x^2y \cdot (-y) = -x^2y^2
\]

2. **Distribute \(2\) to each term in \((x^2 - y)\)**:
\[
2 \cdot x^2 = 2x^2
\]
\[
2 \cdot (-y) = -2y
\]

Now combine all the results from the above steps:

\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Thus, the product of the polynomials \((x^2y + 2)(x^2 - y)\) is:

\[
\boxed{x^4y - x^2y^2 + 2x^2 - 2y}
\]