sat-dog

Choice B is correct. Multiplying (1 – p) by each term of the polynomial within the second pair of parentheses gives (1 – p)1 = 1 – p; (1 – p)p = p – p²; (1 – p)p² = p² – p³; (1 – p)p³ = p³ – p⁴; (1 – p)p⁴ = p⁴ – p⁵; (1 – p)p⁵ = p⁵ – p⁶; and (1 – p)p⁶ = p⁶ – p⁷. Adding these seven expressions together and combining like terms gives 1 + (p – p) + (p² – p²) + (p³ – p³) + (p⁴ – p⁴) + (p⁵ – p⁵) + (p⁶ – p⁶) – p⁷, which can be simplified to 1 – p⁷.

Choices A, C, and D are incorrect and may result from incorrectly identifying the highest power of p in the expressions or incorrectly combining like terms.