Discussion
Expand and simplify (x + y)³
Answer: B
\[ (x+y)^{3} = x^{3} + 3x^{2}y + 3xy^{2} + y^{3} \]
The two middle terms share a factor of \( 3xy \):
\[ 3x^{2}y + 3xy^{2} = 3xy(x + y) \]
\[ \therefore\ (x+y)^{3} = x^{3} + 3xy(x+y) + y^{3} \]
The sign inside the bracket must match the original: \( (x-y)^{3} = x^{3} - 3xy(x-y) - y^{3} \).
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