Question

1-2xy-(x²+y²) factorize it​

Answer 1

Answer:

$\bold\red{(1 + x + y)(1 - x - y)}$

Step-by-step explanation:

Given,

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

Further simplifying,

we get,

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

But,

we know that,

${a}^{2} + 2ab + {b}^{2} = {(a + b)}^{2}$

Therefore,

we get,

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

But,

we know that,

${a}^{2} - {b}^{2} = (a + b)(a - b)$

Therefore,

we get,

$= \bold{(1 + x + y)(1 - x - y)}$