解:?$(2)$?∵?$(a + b)^2 = a^2 + 2ab + b^2$?
已知?$a + b = 10,$??$ab = 16$?
∴?$a^2 + b^2=(a + b)^2 - 2ab = 10^2 - 2×16 = 100 - 32 = 68$?
?$ (3)$?設(shè)?$8 - x = m,$??$x - 2 = n$?
則?$m + n = 8 - x + x - 2 = 6,$??$\mathrm {m^2} + n^2 = 22$?
∵?$(m + n)^2 =\mathrm {m^2} + 2\ \mathrm {m}n + n^2$?
∴?$mn=\frac {(m + n)^2 - (\mathrm {m^2} + n^2)}2=\frac {6^2 - 22}2=\frac {36 - 22}2=7$?
?$ $?即這個(gè)長方形面積為?$7$?