GUYS, PLEASE HELP The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.

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

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step-by-step explanation: