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

Which of the following is an equivalent form of $(1.5x-2.4)^{2}-(5.2x^{2}-6.4)$?

","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-25"}],"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 an equivalent form of $(1.5x-2.4)^{2}-(5.2x^{2}-6.4)$?

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

Choice $\\mathbf{C}$ is correct. The first expression $\\left(1.5x-2.4\\right)^{2}$ can be rewritten as $\\left(1.5x-2.4\\right)\\left(1.5x-2.4\\right)$. Applying the distributive property to this product yields $\\left(2.25x^{2}-3.6x-3.6x+5.76\\right)-\\left(5.2x^{2}-6.4\\right)$. This difference can be rewritten as $\\left(2.25x^{2}-3.6x-3.6x+5.76\\right)+\\left(-1\\right)\\left(5.2x^{2}-6.4\\right)$. Distributing the factor of $\\mathbf{-1}$ through the second expression yields $2.25x^{2}-3.6x-3.6x+5.76-5.2x^{2}+6.4$. Regrouping like terms, the expression becomes $\\left(2.25x^{2}-5.2x^{2}\\right)+\\left(-3.6x-3.6x\\right)+\\left(5.76+6.4\\right)$. Combining like terms yields $-2.95x^{2}-7.2x+12.16$.

Choices A, B, and D are incorrect and likely result from errors made when applying the distributive property or combining the resulting like terms.

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

Which of the following is an equivalent form of $(1.5x-2.4)^{2}-(5.2x^{2}-6.4)$?

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

$-2.2x^{2}+1.6$

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

$-2.2x^{2}+11.2$

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

$-2.95x^{2}-7.2x+0.64$

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

$-2.95x^{2}-7.2x+12.16$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-25"}