Proving and Applying Polynomial Identities Practice Test

Generate a Pythagorean triple using the identity $$ (x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2 $$ with $x=4$ and $y=1$. Which triple $(a,b,c)$ is correct (order of $a,b$ may be swapped)?​

Prove the identity $$ (a-b)^3=a^3-3a^2b+3ab^2-b^3 $$ by expanding the left-hand side. Which expression is the correct expansion of $(a-b)^3$?