Question

factorise x^3-y^3+1+3xy​

Answer 1

${x}^{3} - {y}^{3} + 1 + 3xy$

${x}^{3} + ( { - y}^{3} ) + {1}^{3} - 3(x)( - y)(1)$

using identity

a³ + b³ + c³ - 3xyz = (a + b + c)(a² + b² + c² - ab - bc -ca)

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

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