Question

${x}^{2} - {y }^{2} + 2y - 1$
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Answer 1

Answer:

=X^2-(y^2+2y-1)

=x^2-(y^2+2.y.1-1^2)

=x^2-(y+1)^2

=[x+(y+1)] [x-(y+1)]

=[x+y+1] [x-y-1]

⬆️hope it helps you ☺

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Answer 2

GIVEN:

$x {}^{2} - y {}^{2} + 2y - 1$

TASK : TO FACTORIZE IT

SOLUTION :

$x {}^{2} - (y {}^{2} - 2y + 1) \\ \\ using \: (a - b) {}^{2} = a {}^{2} - 2ab + b {}^{2} \\ \\ x {}^{2} - (y - 1) {}^{2} \\ \\ now \\ using \: a {}^{2} - b {}^{2} = (a + b)(a - b) \\ \\ we \: get \: \\ (x + y - 1)(x - y + 1) \\ thats \: the \: answer$