Algebra 2 Question of the Day

1. 6
2. 15 (correct answer)
3. 20
4. 10

Explanation: This question tests your understanding of the Binomial Theorem—a formula for expanding $(x + y)^n$ using coefficients from Pascal's Triangle, which saves enormous time compared to multiplying out by hand! The Binomial Theorem says $(x + y)^n$ expands to a sum of $n+1$ terms where coefficients come from row $n$ of Pascal's Triangle, $x$-powers decrease from $n$ to 0, and $y$-powers increase from 0 to $n$. For $(x + y)^6$, row 6 of Pascal's Triangle is 1, 6, 15, 20, 15, 6, 1. The term $x^4 y^2$ has $x$ to power 4 and $y$ to power 2 (note: $4 + 2 = 6$), which is the 3rd term in the expansion, so its coefficient is 15. Choice B correctly identifies this coefficient as 15, while Choice A (6) would be the coefficient of $x^5 y$ or $x y^5$, Choice C (20) is the coefficient of $x^3 y^3$, and Choice D (10) doesn't appear in row 6. The expansion recipe using Pascal's Triangle: identify which term you need by looking at the y-power ($y^2$ means 3rd term), then read off the coefficient—systematic and foolproof!