The width of a rectangle is w yards and the length of the rectangle is (3w-4) yards. The perimeter of the rectangle is given by the algebraic expression 2w+2(3w-4). simplify the algebraic expression 2w+2(3w-4) and determine the perimeter of a rectangle whose width w is 2 yards. simplify the algebraic expression 2w+2(3w-4)

1 answer

To simplify the algebraic expression 2w+2(3w-4), we can use the distributive property.
First, distribute the 2 to both terms inside the parentheses:
2w + 2(3w) - 2(4)
Simplifying the values inside the parentheses:
2w + 6w - 8
Combining like terms:
8w - 8
So the simplified algebraic expression is 8w - 8.

To determine the perimeter of a rectangle with width w = 2 yards, we substitute this value into the expression:
8(2) - 8
16 - 8
Perimeter = 8 yards.