Which expression is equal to ${\sin }^{4}A+{\cos }^{4}A$?

${\sin }^{4}A+{\cos }^{4}A=({\sin }^{2}A+{\cos }^{2}A{)}^2-2{\sin }^{2}A{\cos }^{2}A=1-2{\sin }^{2}A{\cos }^{2}A$. The plus-sign version forgets that the cross term must be SUBTRACTED after squaring the sum; answering 1 assumes fourth powers add up like squares. Check at $A=30$ deg: $\frac{1}{16}+\frac{9}{16}=\frac{10}{16}$ and $1-2\times \frac{1}{4}\times \frac{3}{4}=\frac{5}{8}$.