Question

x square +2xy+y square -a square+2ab-b square factorise

Answer 1

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${x}^{2} + 2xy + {y}^{2} - {a}^{2} + 2ab - {b}^{2} \\ \\ ( {x}^{2} + 2xy + {y}^{2} ) + ( - {a}^{2} + 2ab - {b}^{2} ) \\ \\ ({x}^{2} + 2xy + {y}^{2} ) - ( {a}^{2} - 2ab + {b}^{2} ) \\ \\ {((x)}^{2} + 2 \times x \times y + {(y)}^{2} ) - ( {(a)}^{2} - 2 \times a \times b + {(b)}^{2} ) \\ \\ {(x + y)}^{2} - {(a - b)}^{2}$

Now it is in the format a^2 - b^2 . We have to factorise in the format (a + b) (a - b).

$((x + y) + (a - b)) \: \: ((x + y) - (a - b) \\ \\ (x + y + a - b) \: \: (x + y - a + b)$

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