The area of a rectangular athletic field is represented by the expression 16y^7+32y^5+80y^3 square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. Include correct units with your solution.
16y^7+32y^5+80y^3
=16y³(y^4+2y²+5)
One possible set of dimensions is
16y³ m. x (y^4+2y³+5) m.
To represent the area of a rectangular field, we can use the expression 16y^7+32y^5+80y^3 square meters.
To find one possible set of dimensions (length times width) that satisfies this area, we need to factor the given expression.
Let's factor out the common factor of y^3 from each term:
16y^7 + 32y^5 + 80y^3
= y^3(16y^4 + 32y^2 + 80)
Now, let's further factor the expression inside the parenthesis:
16y^4 + 32y^2 + 80 = 16(y^4 + 2y^2 + 5)
So, the factored expression becomes:
16y^7 + 32y^5 + 80y^3 = y^3 * 16(y^4 + 2y^2 + 5)
Now, we can see that the possible dimensions of the rectangular athletic field are:
Length = y^3
Width = 16(y^4 + 2y^2 + 5)
Therefore, the algebraic expression representing one possible set of dimensions of the athletic field is:
Length * Width = y^3 * 16(y^4 + 2y^2 + 5) square meters.