Question

Which expression is equivalent to 24gh - 12g^{2} + 18g

Answer 1

To simplify the expression \( 24gh - 12g^2 + 18g \), we can look for common factors in the terms.

1. First, observe the coefficients of the terms:
- \( 24gh \) has a coefficient of 24.
- \( -12g^2 \) has a coefficient of -12.
- \( 18g \) has a coefficient of 18.

2. The greatest common factor (GCF) of the coefficients 24, -12, and 18 is 6.

3. Now we will factor out the GCF (6) from the expression:

- From \( 24gh \), factoring out \( 6 \) gives \( 6(4h) \).
- From \( -12g^2 \), factoring out \( 6 \) gives \( 6(-2g) \).
- From \( 18g \), factoring out \( 6 \) gives \( 6(3) \).

4. Thus, the expression can be factored as:
\[
6(4gh - 2g^2 + 3g)
\]

So, the expression \( 24gh - 12g^2 + 18g \) can be rewritten as:
\[
6(4gh - 2g^2 + 3g)
\]

This is an equivalent expression to the original one.