Question

Stys

ACA
2. A square with one side length represented by an
expression is shown below.
6(3x + 8) + 32 + 12x
Use the properties of operations to write three
different equivalent expressions to represent the
lengths of the other three sides of the square. One
of your expressions should contain only two terms.

Answer 1

We want to use properties to write expressions for the length of the other sides of the square.

Remember that the length of all the sides in a square is the same, so we only need to rewrite the above expression in two different ways.

First, we can use the distribute property in the first term:

`\sf 6*(3x + 8) + 32 + 12* x`

`\sf = 6*3x + 6*8 + 32 +12* x`

`= \sf 18* x + 48 + 32 + 12* x`

So this can be the length of one of the sides.

Now we can keep simplifying the above equation:

`= \sf 18* x + 48 + 32 + 12* x`

To do it, we can use the distributive and associative property in the next way:

`\sf 18* x + 48 + 32 + 12* x`

`= \sf 18* x + 12* x + 48 + 32`

`= \sf (18* x + 12* x) + (48 + 32)`

`= \sf (18 + 12)* x + 80`

`= \sf 30* x + 80`

This can be the expression to the other side.