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Start with expressions in blue boxes:

1st column) [tex]36x+9;[/tex]

2nd column) [tex]9(4x-1)=36x-9;[/tex]

3rd column) [tex](4\cdot 9x)+(4\cdot 2)=36x+8.[/tex]

You have 6 expressions. Consider all them:

1. [tex]36x+8[/tex] - 3rd column;

2. [tex](9\cdot 4x)+(9\cdot 1)=36x+9[/tex] - 1st column;

3. [tex](3\cdot 12x)-(3\cdot 3)=36x-9[/tex] - 2nd column;

4. [tex]9(4x+1)=36x+9[/tex] - 1st column;

5. [tex]36x-9[/tex] - 2nd column;

6. [tex]4(9x+2)=36x+8[/tex] - 3rd column.

Answer:

The equivalent expressions are:

[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)[/tex]

[tex]9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)[/tex]

[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8[/tex]

Step-by-step explanation:

Consider the provided expressions.

[tex]36x + 9[/tex]

The expression [tex]36x + 9[/tex] can be written as:

[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)[/tex]

[tex]36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)[/tex]

Consider the expression [tex]9(4x-1)[/tex]

The expression [tex]9(4x-1)[/tex] can be written as:

[tex]9(4x-1)=36x-9[/tex]

Take 3 common.

[tex]9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)[/tex]

Consider the expression [tex](4\cdot 9x)+(4\cdot 2)[/tex]

The expression [tex](4\cdot 9x)+(4\cdot 2)[/tex] can be written as:

Take out 4 common

[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)[/tex]

Open the parentheses.

[tex](4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8[/tex]

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