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

Answer 1

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 2

Expand 7/4(8h+3)

Answer 3

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 4

Expand −5/6(9b−12)

Answer 5

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 6

Find the GCF of 20x − 4

Answer 7

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 8

Find the GCF of 30m + 12n

Answer 9

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 10

Factor 8a−28 using the GCF

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: \[ \boxed{4(2a - 7)} \]