Identify all equivalent expressions for:

Question

(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 \(8g^5 - 6g^4\).