Dear Learning Community:
We have been studying the steps necessary to factor an algebraic expression. In addition, we have reviewed multiplying a binomial by another binomial. Below there are three samples of student answers. You will be assigned to evaluate one of the three students work. Please state whether you agree or disagree with this student's work and justify your response.
Student 1: Multiply: (3x + 2)^2 =
(3x + 2) (3x + 2) =
9x^2 + 4
Student 2: Factor completely: 5x^2y - 10xy^2
5x(xy - 2y^2)
Student 3: Factor completely: 5x^3 - 45x =
5x(x^2 - 9) =
5x(x + 3) (x - 3)
Your comments should be received by the close of business on Friday, October 23, 2009.
Sincerely,
Ms. Budney
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Well i think that student#3 work is accurate because when the student broke down the problem the student found the difference of two perfect squares and he showed all his work
ReplyDeleteby nicole hernandez
Akedia witter
ReplyDeleteI agree with student #1 because (3x+2)^2 is (3x+2)(3x+2).And than u combine like terms which is (3X)(3X)= 9X^2,than (2)(2)=4. which makes the expression of 9x^2 + 4.
the answer for number one is 6x-4 i dont really know how to do the rest
ReplyDeletei agree with student number 1 because he/she did 3x * 3x =9x^2(two x's that are mutiplyed is x^2 because the exponent "1" is added to be 2) and 2 times 2 is 4 so he got those right,the answer all together is 9x^2+4 which is correct.
ReplyDeletei think the first answer is right but im not sure. i do think the answer is 9x^2+4.
ReplyDeleteI agree with the answer because 5x(x+3)(-3).-9 is broken dow into (x+3)(x+3). therefore the answer is correct.
ReplyDeleteYes, Student number 2 work is not accurate , Because one of the Y's has Exponent above it. 5x^2y - 10xy^2 the answer to his/her problem is ( I think thats the answer) 5xy(x-2y)
ReplyDeletestudent number 2 is wrong because she/he did not
ReplyDeletefound what goes through 5 and 10. also is a binomial expression. then after you found what goes into 5 and 10 the answer will be 1 and 2. so
then you check your answer if is right or wrong.
and then you distributive property on both side to see or check if they give you the same property.
i chose student #1s works and the reason why i agree that his/her is right because he multiplyed the product together. (3x+2)^2 will give you the same answer as the equation (3x+2)(3x+2) because in the first equation you have to rewrite in twice and solve which is like the second equation 3x x 3x is 9x and 2 x 2 is for so studen ones answer is correct
ReplyDeletethe student number1: I disagree because when you multiply the binomial have two term are multiply.she forgot the forl and she taken the short way and for she did that she forgot. this is my answer .
ReplyDelete(3x+2) (3x+2)
3x(3x+2)=9x^2+6x
2(3x+2)= +6x+4
_________
9x^2+12x+4
the student2: factor completery 5x^y-10xy^2=5x(xy-2y^2)
I disagree because she put the righ equation but she not finish the porblem. i thing the answer is 5xy(x-2y)
5x^2y-10xy^2
the student factor completely i agree because she have her answer correct.5x^3-45X=5X(X+^2-9)=5x(X+3)(X-3)
MY ANSwer is the same that she had.
5x^3-45
5x(x^2-9)
5x(x+3)(x-3)
by:mindre feliz
Dear Nicole,
ReplyDeleteYou are correct that the student realized that there was a difference of two perfect squares. What was the first step that he or she took?
Ms. Budney
Dear Adrian, Akedia, and Jancsi,
ReplyDeleteEach of your explanations of the meaning of (3x+2)^2 is accurate. I also agree with each of the steps you listed however, you are missing some information. Please use your notes and review your work to see if you are able to determine what is missing.
Sincerely,
Ms. Budney
Dear Jeanae,
ReplyDeleteI think you know how to do this problem based on portions of your explanation. Please review what you typed and correct it by posting another comment. In the future, please proof read what you have typed to save you time and energy.
Sincerely,
Ms. Budney
Dear Mindre,
ReplyDeleteYou went above and beyond what was required of you. You have a deep understanding of each problem and you analyzed each student's work perfectly. Congratulations on a job well done.
Sincerely,
Ms. Budney
Dear Andres,
ReplyDeleteYour analysis of the second student's work is perfect. Congratulations on a job well done.
Sincerely,
Ms. Budney
Dear Genesis,
ReplyDeletePlease explain in words the steps necessary to complete the first student's problem. I also want you to review this student's work to see if you are able to determine what is missing.
Sincerely,
Ms. Budney
Dear Kenia,
ReplyDeleteI agree with your explanation regarding how to check your work. However, you also need to make sure that what is in the parantheses has nothing in common. Please review this problem to determine if student 2 could have simplied his or her work further. Please respond to my questions by posting another comment.
Sincerely,
Ms. Budney
Dear Cristina,
ReplyDeletePlease use your notes to complete problem number 1. Then compare your work and answer to the first student's work. Please redo this assignment by posting another comment.
Sincerely,
Ms. Budney
dear,R. Kelly
ReplyDeletefor my assignment i had to see if student number three work was correct for the blog and i strongly agree with their work. the question was telling me to factor 5x^3-45x so first i had to find the greatest factor and i got 5x(x^2-9).i knew it was factor but not completely, so i tried to see if i can brake the problem down even more and i could since their where a perfect square in it,and thats what left me with 5x(x+3)(x-3)
Dear Pilot,
ReplyDeleteYou provided a good explanation of how to complete student three's example. Congratulations on a job well done.
Sincerely,
Ms. Budney
i agree with Student # 1 becausee when you break down the problem which is (3x + 2)^2 this is what you get ..
ReplyDelete(3x + 2)^2 = (3x + 2) (3x + 2)
ANSWER : 9x^2 + 4 .
i Got 9x^2 + 4 because when You mutiply 3x and 3x You would get 9x^2 Because there are 2 x's . And then you would Just have to add 2 + 2 which is 4 .
So ANSWER would be 9x^2 +4 .
YANiBEl A . :]
Yoo i think that the student# # provided a wonderful explanation, and fully understood the concept.His work is accurate
ReplyDeleteDear Yanibel,
ReplyDeleteI agree with your statement regarding the meaning of(3x+2)^2. I would like you to use your notes and review the balance of this student's work to determine what is missing. Then write another post.
Sincerely,
Ms. Budney
Dear Jesus,
ReplyDeleteWhy do you agree with student three's work? You must justify your statement. Please respond to this post.
Sincerely,
Ms. Budney
I agree with student #3's work 5x(x^2-9) beca use the -9 can be can be broken down into -3 and +3. The problem should now look like this
ReplyDelete5x(x-3)(x+3) and 5x is there because it's the GCF. Therefore the answer is correct.
student one is wronq the answer is ; 9x^2 + 12x + 4
ReplyDeleteDear NaNa,
ReplyDeleteWell done. You are correct about the first student's work. Will you please explain to this student exactly where his or her thinking went wrong?
Sincerely,
Ms. Budney
Dear Jeanae,
ReplyDeleteWell done. You did a good job explaining student number three's work. Please continue to infuse mathematical terminology into your writing.
Sincerely,
Ms. Budney
student #1 work is wrong because he didnt foil and he tried to take a short cut this is my answer im not sure if its right
ReplyDelete(3x+2)^2
(3x+2) 3(3x+2)=9x^2+6x
(3x+2) 2(3x+2)=6x+4
9x^2+6x+6x+4
this is my answer--9x^2+12x+4
dear firsttrumpeter
ReplyDeletefor student #1- i disagree with his problem be cause he/she did not use the FOIL method for (3x + 2)^2
(3x + 2) (3x + 2)
9x^2 + 4 to do this problem you need to mulitpy (3x+2)(3x+2) using the foil method. so 3x*3x then 3x into 2 and that will be 9x^2+6x and then mutilpy 2 and 3x and 2*2 and then add and combine those two which will be 9x^2+6x+6x+4= 9x^2+12x+4 that is the answer
instead of usinq distributinq property student one just multiplied the problem.
ReplyDeletei think that studet number 3 is correct because wen u factor 5x^3-45 it becomes 5x(x^2-9) because 5x times x squared equals 5x to the third take away 9 because 5 times negative 9 equals 45, so then that part is correct, but u can factor more so then they put 5x(x+3)(x-3) because 5x times x equals 5x^2 times another x is 5x^3 and positive 3 times negative 3 is negative 9 so it is correct
ReplyDeletei desagree with student number 1 work becase he has wrong answer i got 9x^2+12x+4
ReplyDeleteDear Jancsi,
ReplyDeleteYou are absolutely correct. Congratulations on a job well done.
Sincerely,
Ms. Budney
Dear Yohan,
ReplyDeleteYou are correct. In the future, I want you to explain the step-by-step method you used to get your final answer.
Sincerely,
Ms. Budney