A square with one side length represented by an expression is shown below. Use the DISTRIBUTIVE PROPERTY to write an expression to represent the lengths of the two of the other sides of the square.

By a quick online search I've found that the expression is:

6*(3x + 8) + 32 + 12*x

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:

6*(3x + 8) + 32 + 12*x

= 6*3x + 6*8 + 32 +12*x

= 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:

18*x + 48 + 32 + 12*x

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

18*x + 48 + 32 + 12*x

= 18*x + 12*x + 48 + 32

= (18*x + 12*x) + (48 + 32)

=  (18 + 12)*x + 80

= 30*x + 80

This can be the expression to the other side.

step-by-step explanation:

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