Question

x^4 - y^4 + 2y^2 - 1 factorise ​

Answer 1

$= > {x}^{4} - {y}^{4} + 2 {y}^{2} - 1 \\ = > {x}^{4} - ( {y}^{4} - 2 {y}^{2} + 1) \\ = > {x}^{4} - ( ({y}^{2} {)}^{2} - (2 \times {y}^{2} \times 1) + {(1)}^{2} )\\ = > \bf \color{red}{ {a}^{2} - 2ab + {b}^{2} } = (a + b {)}^{2} \\ = > {x}^{4} - ( {y}^{2} - 1 {)}^{2} \\ = > {( {x}^{2} )}^{2} - ( {y}^{2} - 1 {)}^{2} \\ = > \bf \color{green}{ {a}^{2} - {b}^{2} = (a + b)(a + b) } \\ = > ( {x}^{2} - ( {y}^{2} - 1))( {x}^{2} + (y {}^{2} - 1)) \\ = > \boxed{( {x}^{2} - {y}^{2} + 1)( {x}^{2} + {y}^{2} - 1) }$