Questions: Factor the polynomial completely. [ y^2-1= ]

Transcript text: Factor the polynomial completely. \[ y^{2}-1= \]

Solution

Solution Steps

Step 1: Identify the Polynomial

We start with the polynomial \( y^{2} - 1 \).

Step 2: Recognize the Difference of Squares

The expression \( y^{2} - 1 \) can be recognized as a difference of squares, which follows the identity: \[ a^{2} - b^{2} = (a - b)(a + b) \] where \( a = y \) and \( b = 1 \).

Step 3: Apply the Difference of Squares Formula

Using the difference of squares formula, we can factor \( y^{2} - 1 \) as follows: \[ y^{2} - 1 = (y - 1)(y + 1) \]

Step 4: Present the Fully Factorized Form

Thus, the fully factorized form of the polynomial \( y^{2} - 1 \) is: \[ (y - 1)(y + 1) \]

Final Answer

\(\boxed{(y - 1)(y + 1)}\)

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