Arectangle has length (x-3)² and width 4. the perimeter of the rectangle is 40. find the length.

To work out the length, we just need to multiply 4 by 2, subtract this from 40 and then divide by 2 to get the length

4 x 2 = 8
40 - 8 = 32
32/2 = 16

If, however you want to find x

First step, we want to multiply out the brackets
(x-3)² can also be written as (x-3)(x-3)
Using FOIL, we can expand the double brackets

First
Outer
Inner
Last

F = xx = x²
O = x × -3 = -3x
I = -3 × x = -3x
L = -3 × -3 = 9

Now collect any like terms
x² -6x + 9

x² - 6x + 9 = 16
-9
x² - 6x = 7

Make this equal to 0 and then re-factor
x² - 6x - 7 = 0
Numbers that add to make -6 and multiply to make -7
1 and -7

Re-write with the two factors
x² + x -7x - 7
Split into 2 and factor
x² + x = x(x+1)
-7x - 7 = -7(x+1)
Use the coefficients of the brackets and what is inside to make the new set
(x-7)(x+1)

x = -7 or 1

The second section is only needed if you wanted to find x