Expand (x + y)^4.

Expand (x + y)^4.

• A. x^4 + 3x^3y + 3x^2y^2 + xy^3 + y^4
• B. x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4
• C. x^4 + 4x^3y + 4x^2y^2 + 4xy^3 + y^4
• D. x^4 + 5x^3y + 6x^2y^2 + 5xy^3 + y^4

Answer: (B)

Expanding a binomial to the fourth power uses the binomial theorem, which says the coefficients come from the fourth row of Pascal’s triangle: 1, 4, 6, 4, 1. Each term pairs x and y with exponents that add up to 4: x^4, x^3y, x^2y^2, xy^3, and y^4. Putting these together gives x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4. You can confirm by first squaring to get (x+y)^2 = x^2 + 2xy + y^2, then squaring that result to obtain the same expression. The other options would not match those binomial coefficients for n = 4, missing the 6 or using incorrect multipliers.

Expanding a binomial to the fourth power uses the binomial theorem, which says the coefficients come from the fourth row of Pascal’s triangle: 1, 4, 6, 4, 1. Each term pairs x and y with exponents that add up to 4: x^4, x^3y, x^2y^2, xy^3, and y^4. Putting these together gives x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4. You can confirm by first squaring to get (x+y)^2 = x^2 + 2xy + y^2, then squaring that result to obtain the same expression. The other options would not match those binomial coefficients for n = 4, missing the 6 or using incorrect multipliers.