Factorize the expression (2x − 3y)2 - 4y2.

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To factorize the expression (2x − 3y)² − 4y², we will use the difference of squares formula, a² − b² = (a − b)(a + b). Step 1: Identify a and b in the given expression. Here, a = (2x − 3y) and b² = 4y². Therefore, b = √(4y²) = 2y. Step 2: Apply the difference of squares formula. Substitute a and b into (a − b)(a + b): ((2x − 3y) − 2y)((2x − 3y) + 2y) Step 3: Simplify the terms inside each parenthesis. For the first parenthesis: (2x − 3y − 2y) = (2x − 5y); For the second parenthesis: (2x − 3y + 2y) = (2x − y) Step 4: Write the final factored expression. (2x − 5y)(2x − y) The factored form is: (2x − 5y)(2x − y)

Factorize the expression (2x - 3y)2 - 4y2.

Answer

Step-by-step solution

Identify $a$ and $b$ in the given expression.

Apply the difference of squares formula.

Simplify the terms inside each parenthesis.

Write the final factored expression.

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