The problem is to factor three linear expressions and fill in the blanks with the correct numbers from the given options: 2, 3, 4, 5, 6, 7, 8, 9, 10. The expressions are: $72x - 18 = \Box(\Box x - \Box)$ $35x + 21xy = \Box x (\Box + \Box y)$ $60 - 40x = \Box (\Box - \Box x)$

1. Problem Description

The problem is to factor three linear expressions and fill in the blanks with the correct numbers from the given options: 2, 3, 4, 5, 6, 7, 8, 9,

1

0. The expressions are:

$72x - 18 = \Box(\Box x - \Box)$

$35x + 21xy = \Box x (\Box + \Box y)$

$60 - 40x = \Box (\Box - \Box x)$

2. Solution Steps

First Expression: $72x - 18$

The greatest common factor (GCF) of 72 and 18 is

1

8. $72x - 18 = 18(4x - 1)$

However, 1 is not among the numbers available. Let's check for other common factors.

We could test factors of 18: 2, 3, 6, 9

If we factor out 9: $72x - 18 = 9(8x - 2)$. 2 and 8 are both available. Therefore the solution to the first expression is

$72x - 18 = 9(8x - 2)$

Second Expression: $35x + 21xy$

The GCF of 35 and 21 is

7. We can also factor out $x$.

$35x + 21xy = 7x(5 + 3y)$.

Therefore the solution to the second expression is:

$35x + 21xy = 7x(5 + 3y)$

Third Expression: $60 - 40x$

The GCF of 60 and 40 is

2

0. $60 - 40x = 20(3 - 2x)$.

However, 20 is not in the list. Let's try factoring out

1

0. $60 - 40x = 10(6 - 4x)$

Therefore the solution to the third expression is:

$60 - 40x = 10(6 - 4x)$

3. Final Answer

$72x - 18 = 9(8x - 2)$

$35x + 21xy = 7x(5 + 3y)$

$60 - 40x = 10(6 - 4x)$