Question

Multiply the polynomial (b+8)(3b−6) to simplify.(1 point) Responses b2+30b−48 b squared plus 30 b minus 48 b2+18b−36 b squared plus 18 b minus 36 3b2+18b−48 3 b squared plus 18 b minus 48 3b2+30b−48

Answer 1

What is the product of the polynomials (x2y+2)(x2−y)?(1 point) Responses x4y+x2−2y x superscript 4 baseline y plus x squared minus 2 y x3y−x2y2+2x2−2y x cubed y minus x squared y squared plus 2 x squared minus 2 y x4y−x2y2+2x2−2y x superscript 4 baseline y minus x squared y squared plus 2 x squared minus 2 y x4y−xy+x2y

Answer 2

To multiply the polynomials \((b + 8)(3b - 6)\), we can use the distributive property (also known as the FOIL method for binomials):

\[
(b + 8)(3b - 6) = b \cdot 3b + b \cdot (-6) + 8 \cdot 3b + 8 \cdot (-6)
\]

Calculating each term:

1. \(b \cdot 3b = 3b^2\)
2. \(b \cdot (-6) = -6b\)
3. \(8 \cdot 3b = 24b\)
4. \(8 \cdot (-6) = -48\)

Now, combine the terms:

\[
3b^2 + (-6b + 24b) - 48 = 3b^2 + 18b - 48
\]

So the simplified result is:

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

The correct response is:

**3b² + 18b - 48**

Answer 3

To find the product of the polynomials \((x^2y + 2)(x^2 - y)\), we will use the distributive property:

\[
(x^2y + 2)(x^2 - y) = x^2y \cdot (x^2 - y) + 2 \cdot (x^2 - y)
\]

Now, distribute each term:

1. Distributing \(x^2y\):
\[
x^2y \cdot x^2 = x^4y
\]
\[
x^2y \cdot (-y) = -x^2y^2
\]

So, from \(x^2y \cdot (x^2 - y)\), we get:
\[
x^4y - x^2y^2
\]

2. Distributing \(2\):
\[
2 \cdot x^2 = 2x^2
\]
\[
2 \cdot (-y) = -2y
\]

So, from \(2 \cdot (x^2 - y)\), we get:
\[
2x^2 - 2y
\]

Now we combine all the results:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Putting it all together, the final result is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Among the provided choices, the correct response is:

**x⁴y − x²y² + 2x² − 2y**