Answer:
4x - 1
Step-by-step explanation:
Given the area
16x² - 8x + 1
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 16 × 1 = 16 and sum = - 8
The factors are - 4 and - 4
Use these factors to split the x- term
16x² - 4x - 4x + 1 ( factor the first/second and third/fourth terms )
= 4x(4x - 1) - 1(4x - 1) ← factor out (4x - 1) from each term
= (4x - 1)(4x - 1)
= (4x - 1)²
The area of a square = s² ( where s is the length of the side )
s² = (4x - 1)², thus
s = 4x - 1 ← length of side of square
