Question

1. Resolve into factors a²-b²-c² + d² + 2(bc+ad).​

Answer 1

Answer:

${a}^{2} - {b}^{2} - {c}^{2} + {d}^{2} + 2(bc + ad) \\ = {a}^{2} + {d}^{2} - {c}^{2} - {b}^{2} + 2bc + 2ad \\ = (a { }^{2} + 2ad + {d}^{2} ) - ( {b}^{2} - 2bc + {c}^{2} ) \\ = (a + d) {}^{2} - (b - c) {}^{2} \\ = (a + d - b + c)(a + d + b - c) \\ = (a - b + c + d)(a + b - c + d)$