Factorize the expression x2 + 2xy + y2 - a2.

April 12, 2026Mathematics

ScanSolve AI Answer

April 12, 2026

Answer

(x+y-a)(x+y+a)

Step 1: Factorize the expression $x^2 + 2xy + y^2 - a^2$ . Recognize the first three terms as a perfect square trinomial: $x^2 + 2xy + y^2 = (x+y)^2$ . The expression becomes: $(x+y)^2 - a^2$ This is a difference of squares, $A^2 - B^2 = (A-B)(A+B)$ , where $A = (x+y)$ and $B = a$ . $(x+y-a)(x+y+a)$ The factored form is $\boxed{(x+y-a)(x+y+a)}$ .

Step 2: Factorize the expression

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Factorize the expression x^2 + 2xy + y^2 - a^2. Recognize the first three terms as a perfect square trinomial: x^2 + 2xy + y^2 = (x+y)^2.

Asked on April 12, 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 April 12, 2026

Step 1: Factorize the expression x^2 + 2xy + y^2 - a^2. Recognize the first three terms as a perfect square trinomial: x^2 + 2xy + y^2 = (x+y)^2. The expression becomes: (x+y)^2 - a^2 This is a difference of squares, A^2 - B^2 = (A-B)(A+B), where A = (x+y) and B = a. (x+y-a)(x+y+a) The factored form is (x+y-a)(x+y+a). Step 2: Factorize the expression