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Advanced Math / Equivalent expressions Difficulty: Medium

Which of the following is equivalent to  ?

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Explanation

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.