Question

factorise p^4-(p+q)^4

Answer 1

p^4-(p+q)^4

=(p^2)^2 - {(p+q)^2}^2

={(p^2) + {(p+q)^2} {p^2 - {(p+q)^2}

={(p^2) + {(p+q)^2} {p + (p+q)} {p - (p+q)}

={(p^2) + {(p+q)^2} (2p+q )×-q

= -q(2p+q) {p^2+ {(p+q)^2}