Question

Identify all equivalent expressions for:

(4g−3)(2g4)


Responses

8g
8 g

4×g×g×g×2×g×g×g×g
4×g×g×g×2×g×g×g×g

4×2×g×g×g×gg×g×g
4×2×g×g×g×gg×g×g

8g7

Answer 1

Let's simplify the expression \((4g−3)(2g^4)\) and evaluate which options are equivalent.

1. **Distribute the terms**:
\[
(4g - 3)(2g^4) = 4g \cdot 2g^4 - 3 \cdot 2g^4
\]

2. **Calculate each part**:
\[
4g \cdot 2g^4 = 8g^{1+4} = 8g^5
\]
\[
-3 \cdot 2g^4 = -6g^4
\]

3. **Combine the terms**:
The expression can be represented as:
\[
8g^5 - 6g^4
\]

Now let's compare this with the provided responses:

1. **8g** - No, this does not match.
2. **8 g** - No, this does not match.
3. **\(4 \times g \times g \times g \times 2 \times g \times g \times g \times g\)** - No, this is equal to \(8g^5\), not \(8g^5 - 6g^4\).
4. **\(4 \times 2 \times g \times g \times g \times gg \times g \times g\)** - This simplifies to \(8g^5\) as well, not a match.
5. **\(4 \times 2 \times g \times g \times g \times gg \times g \times g\)** - This is again \(8g^5\), not equivalent to \(8g^5 - 6g^4\).
6. **8g7** - If this means \(8g^7\), it's not equivalent either since our expression contains \(8g^5\) and \(-6g^4\).

None of the provided options are equivalent to the expression \((4g−3)(2g^4)\), which simplifies to \(8g^5 - 6g^4\).