write the expression 12p+48 as a product using the gcf as one of the factors. 12p + 48 = ? (p+?)

Answer 1

To factor the expression \(12p + 48\) using the Greatest Common Factor (GCF), we first identify the GCF of the coefficients 12 and 48.

The factors of 12 are:
\[ 1, 2, 3, 4, 6, 12 \]

The factors of 48 are:
\[ 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 \]

The greatest common factor of 12 and 48 is 12.

So, we factor out 12 from each term of the expression \(12p + 48\):

\[ 12p + 48 = 12(p) + 12(4) \]

\[ 12p + 48 = 12(p + 4) \]

Thus, the expression \(12p + 48\) as a product using the GCF is:

\[ 12(p + 4) \]

Answer 2

which of the following expressions are equivalent to 40x+30y? Choose ALL that apply.

5x(8+6), 5(8x+6y), 10(40x+30y), 10(4x+3y), 2y(20x+15)
or 2(20x+15y)

Answer 3

Let's analyze each given expression to determine whether it is equivalent to \(40x + 30y\):

1. \(5x(8 + 6)\):
- Distribute the \(5x\):
\[ 5x \cdot 8 + 5x \cdot 6 = 40x + 30x = 70x \]
- This expression simplifies to \(70x\), which is not equivalent to \(40x + 30y\).

2. \(5(8x + 6y)\):
- Distribute the \(5\):
\[ 5 \cdot 8x + 5 \cdot 6y = 40x + 30y \]
- This expression simplifies to \(40x + 30y\), which is equivalent.

3. \(10(40x + 30y)\):
- Distribute the \(10\):
\[ 10 \cdot 40x + 10 \cdot 30y = 400x + 300y \]
- This expression simplifies to \(400x + 300y\), which is not equivalent to \(40x + 30y\).

4. \(10(4x + 3y)\):
- Distribute the \(10\):
\[ 10 \cdot 4x + 10 \cdot 3y = 40x + 30y \]
- This expression simplifies to \(40x + 30y\), which is equivalent.

5. \(2y(20x + 15)\):
- Distribute the \(2y\):
\[ 2y \cdot 20x + 2y \cdot 15 = 40xy + 30y \]
- This expression simplifies to \(40xy + 30y\), which is not equivalent to \(40x + 30y\).

6. \(2(20x + 15y)\):
- Distribute the \(2\):
\[ 2 \cdot 20x + 2 \cdot 15y = 40x + 30y \]
- This expression simplifies to \(40x + 30y\), which is equivalent.

Therefore, the expressions that are equivalent to \(40x + 30y\) are:

\[ 5(8x + 6y) \]
\[ 10(4x + 3y) \]
\[ 2(20x + 15y) \]