The perimeter of a square is (16a + 20ab) inches. Factor the expression completely. Does the expression you wrote inside the parentheses show the length of one side of the square? Why or why not. If not how can you determine the length of one side of the square?

If the perimeter of a square is 16a + 20ab inches, then that means that:

1) s + s + s + s = 16a + 20ab

2) s² = 16a + 20ab

Where s represents one side of a square.

Factoring the expression 16a + 20ab. We can factor this binomial using the greatest common factor. What do both terms 16a and 20ab have in common? Theyre both divisible by 4a. So, we can factor out a 4a from the expression.

16a + 20ab

= 4a (4 + 5b)

The expression 4 + 5b does not represent the length of one side of the square. Why? Because if we multiply 4 + 5b by itself, we will not get 16a + 20ab.

(4 + 5b) (4 + 5b)

= 16 + 20b + 20b + 25b²

= 16 + 40b + 25b²

We can, ultimately, determine the length of one side of the square by dividing the expression by 4.

16a + 20ab / 4

= 4 (4a + 5ab) / 4

Cancel out the 4 from the numerator and denominator.

= 4a + 5ab

Check to see if the expression will get you 16a + 20ab.

= (4a + 5ab) (4)

= 16a + 20ab