Mathematics

Expanding a binomial to the third power is about recognizing the pattern in how terms build up. Rather than multiplying $(x-y)(x-y)(x-y)$ three times, you can use the binomial theorem or recall that the coefficients follow Pascal's triangle (1, 3, 3, 1). The key insight is tracking both the powers of $x$ and $y$ as they decrease and increase, and carefully managing the negative sign on $y$ through each term.

Expanding a binomial to the third power is about recognizing the pattern in how terms build up. Rather than multiplying $(x-y)(x-y)(x-y)$ three times, you can use the binomial theorem or recall that the coefficients follow Pascal's triangle (1, 3, 3, 1). The key insight is tracking both the powers of $x$ and $y$ as they decrease and increase, and carefully managing the negative sign on $y$ through each term.