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

$(2x+5)^{2}-(x-2)+2(x+3)$

Which of the following is equivalent to the expression above?

","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-12"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$(2x+5)^{2}-(x-2)+2(x+3)$

Which of the following is equivalent to the expression above?

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

Choice A is correct. The given expression can be rewritten as $(2x+5)^{2}+(-1)(x-2)+2(x+3)$. Applying the distributive property, the expression $(-1)(x-2)+2(x+3)$ can be rewritten as $-1(x)+(-1)(-2)+2(x)+2(3)$, or $-x+2+2x+6$. Adding like terms yields $x+8$. Substituting $x+8$ for $(-1)(x-2)+2(x+3)$ in the given expression yields $(2x+5)^{2}+x+8$. By the rules of exponents, the expression $(2x+5)^{2}$ is equivalent to $(2x+5)(2x+5)$. Applying the distributive property, this expression can be rewritten as $2x(2x)+2x(5)+5(2x)+5(5)$, or $4x^{2}+10x+10x+25$. Adding like terms gives $4x^{2}+20x+25$. Substituting $4x^{2}+20x+25$ for $(2x+5)^{2}$ in the rewritten expression yields $4x^{2}+20x+25+x+8$, and adding like terms yields $4x^{2}+21x+33$.

Choices B, C, and D are incorrect. Choices C and D may result from rewriting the expression $(2x+5)^{2}$ as $4x^{2}+25$, instead of as $4x^{2}+20x+25$. Choices B and C may result from rewriting the expression $-(x-2)$ as $-x-2$, instead of $-x+2$.

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

$(2x+5)^{2}-(x-2)+2(x+3)$

Which of the following is equivalent to the expression above?

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

$4x^{2}+21x+29$

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

$4x^{2}+x+29$

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

$4x^{2}+x+33$

"}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$4x^{2}+21x+33$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-12"}

$(2x+5)^{2}-(x-2)+2(x+3)$Which of the following is equivalent to the expression above?

$(2x+5)^{2}-(x-2)+2(x+3)$Which of the following is equivalent to the expression above?

$(2x+5)^{2}-(x-2)+2(x+3)$Which of the following is equivalent to the expression above?

$(2x+5)^{2}-(x-2)+2(x+3)$

Which of the following is equivalent to the expression above?

$(2x+5)^{2}-(x-2)+2(x+3)$

Which of the following is equivalent to the expression above?

$(2x+5)^{2}-(x-2)+2(x+3)$

Which of the following is equivalent to the expression above?