(p+1)(p+1)(p+1)=ppp+3pp+3p+1 доказать алгебричекое равенство.(q-1)(q-1)(q-1)=qqq-3qq+3q-1

Question

(p+1)(p+1)(p+1)=ppp+3pp+3p+1 доказать алгебричекое равенство.(q-1)(q-1)(q-1)=qqq-3qq+3q-1

Answer 1

(1) (p+1)(p+1)(p+1)=ppp+3pp+3p+1
(p+1)(p+1)(p+1)=
(p²+2p+1)(p+1)=p³+2p²+p+p²+2p+1=p³+3p²+3p+1=ppp+3pp+3p+1
(2) (q-1)(q-1)(q-1)=qqq-3qq+3q-1
(q-1)(q-1)(q-1)=
(q²-2q+1)(q-1)=q³-2q²+q-q²+2q-1=q³-3q²+3q+1=qqq-3qq+3q-1