A rectangle has a length of 6x^3 y^2 - 1 and a width of 3xy + 2. The formula for the perimeter of a rectangle is P=2l + 2w, where l is the length and w is the width. What is the perimeter of the rectangle? Simplify your answer.
P = 2 l + 2 w
P = 2 ( l + w )
P = 2 ( 6 x ^ 3 y ^ 2 - 1 + 3 x y + 2 )
P = 2 ( 6 x ^ 3 y ^ 2 + 3 x y + 1 )
OR
P = 2 ( 6 x ^ 3 y ^ 2 + 3 x y + 1 )
P = 12 x ^ 3 y ^ 2 + 6 x y + 2
P = x y ( 12 x ^ 2 y + 6 ) + 2
OR
P = 6 x y ( 2x ^ 2 y + 1 ) + 2
To find the perimeter of the rectangle, we can use the formula P = 2l + 2w, where l represents the length and w represents the width.
Given:
Length (l) = 6x^3 y^2 - 1
Width (w) = 3xy + 2
Substituting these values into the formula, we have:
P = 2(6x^3 y^2 - 1) + 2(3xy + 2)
Simplifying the equation:
P = 12x^3 y^2 - 2 + 6xy + 4
Combining like terms:
P = 12x^3 y^2 + 6xy + 2
Therefore, the perimeter of the rectangle is 12x^3 y^2 + 6xy + 2.