Question

Factorise: x^2 + 2xy + y^2 - 1

Answer 1

Answer:

${x}^{2} + 2xy + {y}^{2} - 1 \\ = (x + y) {}^{2} - 1 {}^{2} \\ = (x + y + 1)(x + y - 1)$

• In second step , Equation ${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$is used .

• In third step , 1 can be written as $1 {}^{2}$, and I used equation $a {}^{2} - b {}^{2} = (a + b)(a - b)$by taking a = x + y and b = 1.

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