7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 3\",\"description\":\"Equivalent expressions quiz\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-equivalent-expressions-quiz-3\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Advanced Math: Equivalent expressions\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Quiz 3\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-equivalent-expressions-quiz-3\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Quiz 3"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Equivalent expressions quiz

"}}],["$","div",null,{"className":"grid grid-cols-2 md:grid-cols-3 gap-4","children":["$undefined",["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M8.228 9c.549-1.165 2.03-2 3.772-2 2.21 0 4 1.343 4 3 0 1.4-1.278 2.575-3.006 2.907-.542.104-.994.54-.994 1.093m0 3h.01M21 12a9 9 0 11-18 0 9 9 0 0118 0z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Questions"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":10}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M9 12l2 2 4-4m6 2a9 9 0 11-18 0 9 9 0 0118 0z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Level"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Advanced"}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M7 7h.01M7 3h5c.512 0 1.024.195 1.414.586l7 7a2 2 0 010 2.828l-7 7a2 2 0 01-2.828 0l-7-7A1.994 1.994 0 013 12V7a4 4 0 014-4z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Category"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Advanced Math: Equivalent expressions"}]]}]]}]]}]]}]]}],["$","$L17",null,{"quiz":{"id":2504,"prismaId":"cmpz9rki90eg4jglloyiwjhot","slug":"psat-8-9-equivalent-expressions-quiz-3","title":{"rendered":"Quiz 3"},"content":{"rendered":"

Practice on equivalent expressions.

"},"excerpt":{"rendered":"

Equivalent expressions quiz

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Advanced","categorie":"Advanced Math: Equivalent expressions","nombre_questions":10,"score_minimum":80,"ordre_questions":"Fixe","questions":[{"id":"cmrk8ez800x8hjg8wa3yqhrik","texte_question":"

Which expression is equivalent to

$$(x-7)(3x-2y)-6y(-3x+2y)$$?

","type_question":"QCM","explication":"

Distribute the first product.

$$(x-7)(3x-2y)=3x^2-2xy-21x+14y$$

Distribute the second product.

$$-6y(-3x+2y)=18xy-12y^2$$

Add the two results.

$$3x^2-2xy-21x+14y+18xy-12y^2$$

Combine like terms.

$$-2xy+18xy=16xy$$

So, the equivalent expression is:

$$3x^2+16xy-12y^2-21x+14y$$

Final answer: $$3x^2+16xy-12y^2-21x+14y$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$3x^2-2xy-21x+14y+18xy-12y^2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$3x^2+16xy-12y^2-21x+14y$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$3x^2-4xy-12y^2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$3x^2+12xy+12y^2$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez830x8njg8wkbks26er","texte_question":"

In the expression $$4(2x^2+px+5)-8x(p+2)$$, $$p$$ is a constant. This expression is equivalent to $$8x^2-12x+20$$. What is the value of $$p$$?

","type_question":"QCM","explication":"

Expand the expression.

$$4(2x^2+px+5)=8x^2+4px+20$$

Distribute $$-8x$$.

$$-8x(p+2)=-8px-16x$$

Combine the expressions.

$$8x^2+4px+20-8px-16x$$

Combine like terms.

$$8x^2-4px-16x+20$$

Factor the coefficient of $$x$$.

$$8x^2+(-4p-16)x+20$$

The expression is equivalent to:

$$8x^2-12x+20$$

Set the coefficients of $$x$$ equal.

$$-4p-16=-12$$

Add $$16$$ to both sides.

$$-4p=4$$

Divide by $$-4$$.

$$p=-1$$

Final answer: $$-1$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$-2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$-1$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$3$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez850x8tjg8wuw3u0s0p","texte_question":"

$$(ax+2)(4x^2-bx+3)=8x^3+4x^2+2x+6$$

The equation above is true for all $$x$$. What is the value of $$ab$$?

","type_question":"QCM","explication":"

Expand the left side.

$$(ax+2)(4x^2-bx+3)=4ax^3-abx^2+3ax+8x^2-2bx+6$$

Combine like terms.

$$4ax^3+(8-ab)x^2+(3a-2b)x+6$$

Match the coefficient of $$x^3$$.

$$4a=8$$ Divide by $$4$$.

$$a=2$$

Match the coefficient of $$x$$.

$$3a-2b=2$$

Substitute $$a=2$$.

$$3(2)-2b=2$$

Simplify.

$$6-2b=2$$

Subtract $$6$$ from both sides.

$$-2b=-4$$

Divide by $$-2$$.

$$b=2$$

Find $$ab$$.

$$ab=(2)(2)$$

$$ab=4$$

Final answer: $$4$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$3$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$4$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$8$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez890x8zjg8w88q422y2","texte_question":"

The expression $$72y^5-24y^4$$ is equivalent to $$ry^4(3y-1)$$, where $$r$$ is a constant. What is the value of $$r$$?

","type_question":"QCM","explication":"

Factor the greatest common factor from $$72y^5-24y^4$$.

The greatest common factor is $$24y^4$$.

$$72y^5-24y^4=24y^4(3y-1)$$

Compare this with the given expression.

$$ry^4(3y-1)$$

So: $$r=24$$

Final answer: $$24$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$12$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$24$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$48$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$72$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez8c0x95jg8ww4riqqjg","texte_question":"

Which of the following expressions is equivalent to $$x^2-16$$?

","type_question":"QCM","explication":"

Recognize the expression as a difference of squares.

$$x^2-16=x^2-4^2$$

Use the identity:

$$a^2-b^2=(a-b)(a+b)$$

Here,

$$a=x$$ and $$b=4$$.

So:

$$x^2-16=(x-4)(x+4)$$

Final answer: $$(x+4)(x-4)$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$(x+4)^2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$(x-4)^2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(x+4)(x-4)$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(x+8)(x-2)$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez8f0x9bjg8wcu1qvz3z","texte_question":"

$$(4200+50y^2)+5(10y^2-40)$$

The expression above can be written in the form $$ay^2+b$$, where $$a$$ and $$b$$ are constants. What is the value of $$a+b$$?

","type_question":"QCM","explication":"

Distribute $$5$$.

$$5(10y^2-40)=50y^2-200$$

Substitute this into the expression.

$$(4200+50y^2)+50y^2-200$$

Combine like terms.

$$50y^2+50y^2=100y^2$$

$$4200-200=4000$$

So, the expression becomes:

$$100y^2+4000$$

Compare with $$ay^2+b$$.

$$a=100$$

$$b=4000$$

Find $$a+b$$.

$$a+b=100+4000$$

$$a+b=4100$$

Final answer: $$4100$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$100$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$4000$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$4100$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$4200$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez8j0x9hjg8wtl9xv4uv","texte_question":"

Which of the following expressions has a factor of $$x+3$$?

","type_question":"QCM","explication":"

Factor each expression or test for the factor $$x+3$$.

An expression has a factor of $$x+3$$ if substituting $$x=-3$$ gives $$0$$.

Test $$2x^2+12x+18$$.

$$2(-3)^2+12(-3)+18$$

$$2(9)-36+18$$

$$18-36+18=0$$

So, $$x+3$$ is a factor.

Factor the expression.

$$2x^2+12x+18=2(x^2+6x+9)$$

$$2(x^2+6x+9)=2(x+3)^2$$

Final answer: $$2x^2+12x+18$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$2x^2+9x+18$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$2x^2+12x+18$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2x^2+15x+20$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2x^2+18x+18$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez8m0x9njg8wjl6npglx","texte_question":"

Which of the following is equivalent to $$(1-t)(1+t+t^2+t^3+t^4)$$?

","type_question":"QCM","explication":"

Distribute $$1-t$$.

$$(1-t)(1+t+t^2+t^3+t^4)$$

Multiply by $$1$$.

$$1+t+t^2+t^3+t^4$$

Multiply by $$-t$$.

$$-t-t^2-t^3-t^4-t^5$$

Add the terms.

$$1+t+t^2+t^3+t^4-t-t^2-t^3-t^4-t^5$$

Cancel opposite terms.

$$t-t=0$$

$$t^2-t^2=0$$

$$t^3-t^3=0$$

$$t^4-t^4=0$$

The expression becomes:

$$1-t^5$$

Final answer: $$1-t^5$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$1-t^4$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$1-t^5$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$1-t^6$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$1-t^3$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez8p0x9tjg8wl15xvz9v","texte_question":"

The expression $$\\frac{1}{2}x^2-8$$ can be rewritten as $$\\frac{1}{2}(x-k)(x+k)$$, where $$k$$ is a positive constant. What is the value of $$k$$?

","type_question":"QCM","explication":"

Factor out $$\\frac{1}{2}$$.

$$\\frac{1}{2}x^2-8=\\frac{1}{2}(x^2-16)$$

Rewrite $$16$$ as $$4^2$$.

$$x^2-16=x^2-4^2$$

Use the difference of squares identity.

$$x^2-4^2=(x-4)(x+4)$$

So:

$$\\frac{1}{2}x^2-8=\\frac{1}{2}(x-4)(x+4)$$

Compare with:

$$\\frac{1}{2}(x-k)(x+k)$$

So:

$$k=4$$

Final answer: $$4$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$4$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\sqrt{8}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$8$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ez8s0x9zjg8w2ymwyndn","texte_question":"

Which expression is equivalent to $$\\frac{30a}{k}+30ak$$, where $$k$$>$$0$$?

","type_question":"QCM","explication":"

Start with the expression.

$$\\frac{30a}{k}+30ak$$

Rewrite $$30ak$$ with denominator $$k$$.

$$30ak=\\frac{30ak^2}{k}$$

Now add the fractions.

$$\\frac{30a}{k}+\\frac{30ak^2}{k}=\\frac{30a+30ak^2}{k}$$

Factor $$30a$$ from the numerator.

$$\\frac{30a(1+k^2)}{k}$$

Final answer: $$\\frac{30a(1+k^2)}{k}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\frac{30a(1+k^2)}{k}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{30ak^2}{k}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{30a(k+1)}{k}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{60a}{k}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["advanced-math-equivalent-expressions"],"date":"2026-06-04T09:04:47.505Z","modified":"2026-07-14T05:49:52.458Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L18",null,{"targetType":"quiz","targetSlug":"psat-8-9-equivalent-expressions-quiz-3"}]}]]}]}]]

Quiz 3

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