Question

pq^4– p(p – q)^4 factorise it​

Answer 1

Answer...

$\sf \: {pq}^{4} - p {(p - q)}^{4} \\ \\ \sf = p[ {q}^{4} - {(p - q)}^{4}] \\ \\ \sf = p[ {q}^{2} + {(p - q)}^{2}] [ {q}^{2} - {(p - q)}^{2} ] \\ \\ \sf = p[ {p}^{2} + {2q}^{2} - 2pq](q + p - q)(q + p - q) \\ \\ \sf = p({p}^{2} + {2q}^{2} - 2pq)\: p(2q - p) \\ \\ \sf = p( {p}^{2} + {2q}^{2} - 2pq) \: (2q - p)$