The problem asks us to factor linear expressions by filling in the blanks. The three expressions are: 1. $14n - 21 = 7(2n - \_\_\_)$

1. Problem Description

The problem asks us to factor linear expressions by filling in the blanks. The three expressions are:

1. $14n - 21 = 7(2n - \_\_\_)$

2. $32ab - 24a = \_\_\_ a(4b - 3)$

3. $15 - 30y = 5(\_\_\_ - 6y)$

2. Solution Steps

Expression 1: $14n - 21 = 7(2n - \_\_\_)$

We can divide each term in the original expression by 7 to find the missing term.

$14n / 7 = 2n$

$21 / 7 = 3$

So the missing term is

3.

Expression 2: $32ab - 24a = \_\_\_ a(4b - 3)$

We need to find the number that multiplies $4b$ to give $32b$ and multiplies $-3$ to give $-24$. Looking at the $b$ term we need the term outside to be $8$. Let's confirm the other term, $8 * -3 = -24$.

So the missing term is

8.

Expression 3: $15 - 30y = 5(\_\_\_ - 6y)$

We can divide each term in the original expression by 5 to find the missing term.

$15 / 5 = 3$

$30y / 5 = 6y$

So the missing term is

3.

3. Final Answer

1. $14n - 21 = 7(2n - 3)$

2. $32ab - 24a = 8a(4b - 3)$

3. $15 - 30y = 5(3 - 6y)$