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

May 14, 2026Mathematics

ScanSolve AI Answer

May 14, 2026

Answer

(2x - 5y)(2x - y)

Alright manjay9804398176 — let's do this.

To factorize the expression $(2x - 3y)^2 - 4y^2$ , we will use the difference of squares formula, $a^2 - b^2 = (a - b)(a + b)$ .

Step 1: Identify $a$ and $b$ in the given expression. Here, $a = (2x - 3y)$ and $b^2 = 4y^2$ . Therefore, $b = \sqrt{4y^2} = 2y$ .

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: $\boxed{*(2x - 5y)(2x - y)*}$ Send me the next one 📸

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Quick Answer

Alright manjay9804398176 — let's do this. To factorize the expression (2x - 3y)^2 - 4y^2, we will use the difference of squares formula, a^2 - b^2 = (a - b)(a + b).

Asked on May 14, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 14, 2026

Alright manjay9804398176 — let's do this. To factorize the expression (2x - 3y)^2 - 4y^2, we will use the difference of squares formula, a^2 - b^2 = (a - b)(a + b). Step 1: Identify a and b in the given expression. Here, a = (2x - 3y) and b^2 = 4y^2. Therefore, b = sqrt(4y^2) = 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) Send me the next one 📸