Questions: 25z^2-4y^2

Transcript text: 25 z^{2}-4 y^{2}

Solution

Solution Steps

Step 1: Identify the Polynomial

We start with the polynomial expression: \[ 25 z^{2} - 4 y^{2} \]

Step 2: Recognize the Difference of Squares

The expression \(25 z^{2} - 4 y^{2}\) can be recognized as a difference of squares, which follows the formula: \[ a^{2} - b^{2} = (a - b)(a + b) \] where \(a = 5z\) and \(b = 2y\).

Step 3: Apply the Difference of Squares Formula

Using the difference of squares formula, we can factor the polynomial: \[ 25 z^{2} - 4 y^{2} = (5z)^{2} - (2y)^{2} = (5z - 2y)(5z + 2y) \]

Step 4: Present the Final Factorization

Thus, the fully factorized form of the polynomial is: \[ (5z - 2y)(5z + 2y) \]

Final Answer

\(\boxed{(5z - 2y)(5z + 2y)}\)

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