Question

Expand 1/2(8h+4) .(1 point)
Answer
Expand  −5/6  (6b−12) (1 point)
Answer
Find the GCF of 20x−4
Answer
Find the GCF OF 30m+12n
Answer
Factor  8a−28  using the GCF.(1 point)
Answer
Factor 12y + 6
Answered by GPT-4o mini
To expand the expression \(\frac{1}{2}(8h + 4)\), you can distribute \(\frac{1}{2}\) to both terms inside the parentheses:

\[
\frac{1}{2}(8h) + \frac{1}{2}(4)
\]

Calculating each term:

1. \(\frac{1}{2} \times 8h = 4h\)
2. \(\frac{1}{2} \times 4 = 2\)

Now, combine the results:

\[
4h + 2
\]

So, the expanded form of \(\frac{1}{2}(8h + 4)\) is:

\[
\boxed{4h + 2}
\]
Answered by GPT-4o mini
To expand the expression \(-\frac{5}{6}(6b - 12)\), distribute \(-\frac{5}{6}\) to both terms inside the parentheses:

\[
-\frac{5}{6}(6b) + (-\frac{5}{6})(-12)
\]

Now, calculate each term:

1. \(-\frac{5}{6} \times 6b = -5b\)
2. \(-\frac{5}{6} \times -12 = \frac{5}{6} \times 12 = \frac{60}{6} = 10\)

Now, combine the results:

\[
-5b + 10
\]

So, the expanded form of \(-\frac{5}{6}(6b - 12)\) is:

\[
\boxed{-5b + 10}
\]
Answered by GPT-4o mini
To find the Greatest Common Factor (GCF) of the expression \(20x - 4\), we first identify the coefficients and terms in the expression:

1. The coefficients are \(20\) for \(20x\) and \(-4\) for \(-4\).

Next, we find the GCF of the coefficients \(20\) and \(4\):

- The factors of \(20\) are \(1, 2, 4, 5, 10, 20\).
- The factors of \(4\) are \(1, 2, 4\).

The largest common factor between \(20\) and \(4\) is \(4\).

Next, we also check the variable part. Since the term \(20x\) has the variable \(x\) and the term \(-4\) does not have any variable factor, we can conclude that \(x\) is not part of the GCF.

Thus, the GCF of the expression \(20x - 4\) is:

\[
\boxed{4}
\]
Answered by GPT-4o mini
To find the greatest common factor (GCF) of the expression \(30m + 12n\), we will identify the coefficients of both terms and find their GCF.

1. **Coefficients**: The coefficients are \(30\) (from \(30m\)) and \(12\) (from \(12n\)).

2. **Find the GCF of the coefficients**:
- Factors of \(30\): \(1, 2, 3, 5, 6, 10, 15, 30\)
- Factors of \(12\): \(1, 2, 3, 4, 6, 12\)

The common factors of \(30\) and \(12\) are \(1, 2, 3, 6\). Therefore, the largest common factor is \(6\).

3. **Variables**: The terms \(30m\) and \(12n\) have different variable factors (\(m\) and \(n\)). Since they do not share a common variable, we do not include any variables in the GCF.

Thus, the GCF of the expression \(30m + 12n\) is:

\[
\boxed{6}
\]
Answered by GPT-4o mini
To factor the expression \(8a - 28\) using the greatest common factor (GCF), follow these steps:

1. **Find the GCF of the coefficients**:
- The coefficients are \(8\) and \(-28\).
- The factors of \(8\) are \(1, 2, 4, 8\).
- The factors of \(28\) are \(1, 2, 4, 7, 14, 28\).
- The common factors are \(1, 2, 4\), so the GCF is \(4\).

2. **Factor out the GCF**:
- Divide each term by the GCF \(4\):
\[
8a \div 4 = 2a
\]
\[
-28 \div 4 = -7
\]

3. **Write the factored form**:
Thus, you can write the expression as:
\[
8a - 28 = 4(2a - 7)
\]

So, the factored form of \(8a - 28\) is:

\[
\boxed{4(2a - 7)}
\]
Answered by GPT-4o mini
To factor the expression \(12y + 6\) using the greatest common factor (GCF), follow these steps:

1. **Find the GCF of the coefficients**:
- The coefficients are \(12\) and \(6\).
- The factors of \(12\) are \(1, 2, 3, 4, 6, 12\).
- The factors of \(6\) are \(1, 2, 3, 6\).
- The common factors are \(1, 2, 3, 6\), so the GCF is \(6\).

2. **Factor out the GCF**:
- Divide each term by the GCF \(6\):
\[
12y \div 6 = 2y
\]
\[
6 \div 6 = 1
\]

3. **Write the factored form**:
Thus, you can write the expression as:
\[
12y + 6 = 6(2y + 1)
\]

So, the factored form of \(12y + 6\) is:

\[
\boxed{6(2y + 1)}
\]