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