Question

Expand 74(8h+3). (1 point).

Answer 1

Expand 7/4(8h+3)

Answer 2

Expand −5/6(9b−12)

Answer 3

Find the GCF of 20x − 4

Answer 4

Find the GCF of 30m + 12n

Answer 5

Factor 8a−28 using the GCF

Answer 6

To expand the expression \( 74(8h + 3) \), you will distribute \( 74 \) to both terms within the parentheses.

Here’s how it's done:

1. Multiply \( 74 \) by \( 8h \):
\[
74 \times 8h = 592h
\]

2. Multiply \( 74 \) by \( 3 \):
\[
74 \times 3 = 222
\]

Now, combine these results:
\[
74(8h + 3) = 592h + 222
\]

Thus, the expanded form is:
\[
\boxed{592h + 222}
\]

Answer 7

To expand the expression \(\frac{7}{4}(8h + 3)\), you will distribute \(\frac{7}{4}\) to both terms inside the parentheses.

Here’s the step-by-step process:

1. Multiply \(\frac{7}{4}\) by \(8h\):
\[
\frac{7}{4} \times 8h = \frac{7 \times 8h}{4} = \frac{56h}{4} = 14h
\]

2. Multiply \(\frac{7}{4}\) by \(3\):
\[
\frac{7}{4} \times 3 = \frac{7 \times 3}{4} = \frac{21}{4}
\]

Now, combine these results:
\[
\frac{7}{4}(8h + 3) = 14h + \frac{21}{4}
\]

Thus, the expanded form is:
\[
\boxed{14h + \frac{21}{4}}
\]

Answer 8

To expand the expression \(-\frac{5}{6}(9b - 12)\), distribute \(-\frac{5}{6}\) to both terms inside the parentheses.

Here’s how it’s done step-by-step:

1. Multiply \(-\frac{5}{6}\) by \(9b\):
\[
-\frac{5}{6} \times 9b = -\frac{45b}{6} = -\frac{15b}{2} \quad(\text{after simplifying } \frac{45}{6} = \frac{15}{2})
\]

2. Multiply \(-\frac{5}{6}\) by \(-12\):
\[
-\frac{5}{6} \times -12 = \frac{5 \times 12}{6} = \frac{60}{6} = 10
\]

Now, combine these results:
\[
-\frac{5}{6}(9b - 12) = -\frac{15b}{2} + 10
\]

Thus, the expanded form is:
\[
\boxed{-\frac{15b}{2} + 10}
\]

Answer 9

To find the greatest common factor (GCF) of the expression \(20x - 4\), we first look for the GCF of the coefficients and any common terms.

1. **Identify the coefficients**: The coefficients in the expression are \(20\) (from \(20x\)) and \(-4\).
2. **Find the GCF of these coefficients**:
- The factors of \(20\) are \(1, 2, 4, 5, 10, 20\).
- The factors of \(-4\) are \(1, 2, 4\).
- The common factors are \(1, 2, 4\).
- The greatest of these common factors is \(4\).

3. **Factor out the GCF**: Now we can factor out \(4\) from the expression \(20x - 4\):
\[
20x - 4 = 4(5x - 1)
\]

Thus, the GCF of the expression \(20x - 4\) is:
\[
\boxed{4}
\]

Answer 10

To find the greatest common factor (GCF) of the expression \(30m + 12n\), we will look at the coefficients \(30\) and \(12\) and find any common factors.

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

2. **Find the factors of each coefficient**:
- The factors of \(30\) are \(1, 2, 3, 5, 6, 10, 15, 30\).
- The factors of \(12\) are \(1, 2, 3, 4, 6, 12\).

3. **Identify the common factors**: The common factors of \(30\) and \(12\) are \(1, 2, 3, 6\).

4. **Determine the GCF**: The greatest common factor among these is \(6\).

Thus, the GCF of the expression \(30m + 12n\) is:
\[
\boxed{6}
\]

Answer 11

To factor the expression \(8a - 28\) using the greatest common factor (GCF), follow these steps:

1. **Identify the coefficients**: The coefficients in the expression are \(8\) (from \(8a\)) and \(-28\).

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

3. **Factor out the GCF**: Now we can factor \(4\) out of the expression:
\[
8a - 28 = 4(2a - 7)
\]

Thus, the factored form of \(8a - 28\) using the GCF is:
\[
\boxed{4(2a - 7)}
\]