Question

Drag each expression to show whether it is equivalent to 36x + 9, 9(4x – 1), or (4 • 9x) + (4 • 2).

Answer 1

The equivalent expressions are:

`36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)`

`9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)`

`(4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8`

Explanation:

Consider the provided expressions.

`36x + 9`

The expression
`36x + 9` can be written as:

`36x + 9=(9\cdot 4x) + (9\cdot 1)`

`36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)`

Consider the expression
`9(4x-1)`

The expression
`9(4x-1)` can be written as:

`9(4x-1)=36x-9`

Take 3 common.

`9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)`

Consider the expression
`(4\cdot 9x)+(4\cdot 2)`

The expression
`(4\cdot 9x)+(4\cdot 2)` can be written as:

Take out 4 common

`(4\cdot 9x)+(4\cdot 2)=4(9x+2)`

Open the parentheses.

`(4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8`

Answer 2

Start with expressions in blue boxes:

1st column)
`36x+9;`

2nd column)
`9(4x-1)=36x-9;`

3rd column)
`(4\cdot 9x)+(4\cdot 2)=36x+8.`

You have 6 expressions. Consider all them:

1.
`36x+8` - 3rd column;

2.
`(9\cdot 4x)+(9\cdot 1)=36x+9` - 1st column;

3.
`(3\cdot 12x)-(3\cdot 3)=36x-9` - 2nd column;

4.
`9(4x+1)=36x+9` - 1st column;

5.
`36x-9` - 2nd column;

6.
`4(9x+2)=36x+8` - 3rd column.