Question

Multiply polynomial (b + 8)(3b - 6) to simplify (point ) 6 ^ 2 + 185 - 36; 30 ^ 2 + 300 - 48; 3b ^ 2 / 18 * b - 48; 6 ^ 2 + 306 - 48

Answer 1

Let's break down your request step by step.

First, we'll multiply the polynomial \((b + 8)(3b - 6)\):

1. **Using the distributive property (also known as the FOIL method for polynomials)**:
- First: \(b \cdot 3b = 3b^2\)
- Outside: \(b \cdot -6 = -6b\)
- Inside: \(8 \cdot 3b = 24b\)
- Last: \(8 \cdot -6 = -48\)

Now combining these results:
\[
3b^2 + 24b - 6b - 48
\]
Combine like terms:
\[
3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48
\]

So, \((b + 8)(3b - 6) = 3b^2 + 18b - 48\).

Next, let's simplify the different expressions you provided:

1. **Expression 1: \(6^2 + 185 - 36\)**
\[
6^2 = 36 \implies 36 + 185 - 36 = 185
\]

2. **Expression 2: \(30^2 + 300 - 48\)**
\[
30^2 = 900 \implies 900 + 300 - 48 = 1152
\]

3. **Expression 3: \(\frac{3b^2}{18} \cdot b - 48\)**
\[
\frac{3b^2}{18} = \frac{1}{6}b^2 \implies \frac{1}{6}b^2 \cdot b - 48 = \frac{1}{6}b^3 - 48
\]

4. **Expression 4: \(6^2 + 306 - 48\)**
\[
6^2 = 36 \implies 36 + 306 - 48 = 294
\]

To summarize the results:
- The polynomial multiplication gives: **\(3b^2 + 18b - 48\)**
- Expressions evaluated:
- \(6^2 + 185 - 36 = 185\)
- \(30^2 + 300 - 48 = 1152\)
- \(\frac{3b^2}{18} \cdot b - 48 = \frac{1}{6}b^3 - 48\)
- \(6^2 + 306 - 48 = 294\)