Expand −

Question

5
6
(9b − 12). Fill in the blanks to complete the expanded expression. (1 point)

b +

Answer 1

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

1. Distributing \( \frac{5}{6} \) to \( 9b \): \[ \frac{5}{6} \cdot 9b = \frac{45}{6}b = 7.5b \]

2. Distributing \( \frac{5}{6} \) to \( -12 \): \[ \frac{5}{6} \cdot -12 = -\frac{60}{6} = -10 \]

Combining both parts, the expanded expression is: \[ 7.5b - 10 \]

So, to fill in the blank, the complete expression is: \[ b + \text{(fill in the blank)} = 7.5b - 10 \]

Thus, the answer for the blank would be: \[ -10 \]

Answer 2

there are 2 blanks!!

Answer 3

I apologize for the oversight! Let me re-evaluate the expansion of \( \frac{5}{6}(9b - 12) \) and fill in two blanks correctly.

First, we expand:

1. Distributing \( \frac{5}{6} \) to \( 9b \): \[ \frac{5}{6} \cdot 9b = \frac{45}{6}b = 7.5b \]

2. Distributing \( \frac{5}{6} \) to \( -12 \): \[ \frac{5}{6} \cdot -12 = -\frac{60}{6} = -10 \]

So the expanded expression is: \[ 7.5b - 10 \]

Since we need to present this with two blanks, we can rewrite it in terms of \( b \):

\[ 7.5b + (-10) \]

Thus, we can look at it as: \[ b + (6.5b - 10) \]

In this representation:

• The first blank would be \( 6.5b \)
• The second blank would be \(-10\)

So, the filled blanks would be:

\[ b + 6.5b - 10 \]

Therefore, to summarize, the two blanks are:

1. 6.5b
2. -10

Thank you for your patience!

Answer 4

Find the GCF of 20x − 4. (1 point)

Answer 5

To find the greatest common factor (GCF) of the expression \(20x - 4\), we can start by identifying the coefficients and constants involved.

1. The coefficients are 20 and -4.
2. The GCF of 20 and 4 can be found as follows:
   • 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 factors is 4.

Now, we can also factor out the GCF from the expression:

\[ 20x - 4 = 4(5x - 1) \]

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

Answer 6

Find the GCF of 30m + 12n. (1 point)

Answer 7

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

1. Find the GCF of the coefficients:

   • The factors of \(30\) are: \(1, 2, 3, 5, 6, 10, 15, 30\)
   • The factors of \(12\) are: \(1, 2, 3, 4, 6, 12\)
   • The common factors are: \(1, 2, 3, 6\)
   • The greatest of these factors is 6.

2. Factor the GCF out of the expression: \[ 30m + 12n = 6(5m + 2n) \]

Thus, the GCF of \(30m + 12n\) is 6.

Answer 8

Factor 8a − 28 using the GCF. (1 point)

Answer 9

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

1. Find the GCF of the coefficients (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: \(1, 2, 4\)
   • The greatest of these factors is 4.

2. Factor out the GCF from the expression: \[ 8a - 28 = 4(2a - 7) \]

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

Answer 10

Factor 12y + 6 using the GCF. (1 point)

Answer 11

To factor the expression \(12y + 6\) using the greatest common factor (GCF), follow these steps:

1. Find the GCF of the coefficients (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: \(1, 2, 3, 6\)
   • The greatest of these factors is 6.

2. Factor out the GCF from the expression: \[ 12y + 6 = 6(2y + 1) \]

Thus, the factored form of \(12y + 6\) is: \[ 6(2y + 1) \]