{"@context":"https://schema.org/","@type":"Quiz","name":"

Which of the following is equivalent to

$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-167"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

Which of the following is equivalent to

$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

","comment":{"@type":"Comment","text":"

Choice B is correct. Multiplying $(1 – p)$ by each term of the polynomial within the second pair of parentheses gives

$(1– p)1 = 1 – p$

$(1 – p)p = p – p^{2}$

$(1 – p)p^{2} = p^{2} – p^{3}$

$(1 – p)p^{3} = p^{3} – p^{4}$

$(1 – p)p^{4} = p^{4} – p^{5}$

$(1 – p)p^{5} = p^{5} – p^{6}$

$(1 – p)p^{6} = p^{6} – p^{7}$

Adding these seven expressions together and combining like terms gives

$1 + (p – p) + (p^{2} – p^{2})+ (p^{3} – p^{3}) + (p^{4} – p^{4}) + (p^{5} – p^{5}) + (p^{6} – p^{6}) – p^{7}$

which can be simplified to $1 – p^{7}$.

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.

"},"encodingFormat":"text/markdown","text":"

Which of the following is equivalent to

$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$1-p^{8}$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$1-p^{6}$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$1-p^{5}$

"}],"acceptedAnswer":{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$1-p^{7}$

","comment":{"@type":"Comment","text":"

Choice B is correct. Multiplying $(1 – p)$ by each term of the polynomial within the second pair of parentheses gives

$(1– p)1 = 1 – p$

$(1 – p)p = p – p^{2}$

$(1 – p)p^{2} = p^{2} – p^{3}$

$(1 – p)p^{3} = p^{3} – p^{4}$

$(1 – p)p^{4} = p^{4} – p^{5}$

$(1 – p)p^{5} = p^{5} – p^{6}$

$(1 – p)p^{6} = p^{6} – p^{7}$

Adding these seven expressions together and combining like terms gives

$1 + (p – p) + (p^{2} – p^{2})+ (p^{3} – p^{3}) + (p^{4} – p^{4}) + (p^{5} – p^{5}) + (p^{6} – p^{6}) – p^{7}$

which can be simplified to $1 – p^{7}$.

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.

"},"answerExplanation":{"@type":"Comment","text":"

Choice B is correct. Multiplying $(1 – p)$ by each term of the polynomial within the second pair of parentheses gives

$(1– p)1 = 1 – p$

$(1 – p)p = p – p^{2}$

$(1 – p)p^{2} = p^{2} – p^{3}$

$(1 – p)p^{3} = p^{3} – p^{4}$

$(1 – p)p^{4} = p^{4} – p^{5}$

$(1 – p)p^{5} = p^{5} – p^{6}$

$(1 – p)p^{6} = p^{6} – p^{7}$

Adding these seven expressions together and combining like terms gives

$1 + (p – p) + (p^{2} – p^{2})+ (p^{3} – p^{3}) + (p^{4} – p^{4}) + (p^{5} – p^{5}) + (p^{6} – p^{6}) – p^{7}$

which can be simplified to $1 – p^{7}$.

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.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-167"}

Which of the following is equivalent to$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

Which of the following is equivalent to$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

Which of the following is equivalent to$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

Which of the following is equivalent to

$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

Which of the following is equivalent to

$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?

Which of the following is equivalent to

$(1-p)(1+p+p^{2}+p^{3}+p^{4}+p^{5}+p^{6})$?