This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
I'm also having trouble with #53.. Your hint didn't help at all.. ;) The wording troubles me, I don't understand what I am supposed to do. "Write a second expression for the area of the square labeled (a-b)^2"? I understand how you get the area, a^2, from looking at the sides.
If the equation was something like 24x^4 + 8x^2, would you be able to reduce it to something like 3x^4 + x^2 by dividing both monomials by 8 or would that not be the same?
For #25, on the Mid-Chapter Quiz, I have a feeling it is yes, but seeing we have not done any negative monomial/polynomial work I also have a feeling that it is no.. But if all of the exponents were negative then yes the degree could as well be negative!
Draw yourself a separate area model depicting (6+4)(7+3). Put 6 and +4 as the length (bottom) and put 7 and 3 as the width (aka height on the left).
Clearly, the area of the lower left sub-rectangle is 6*12=72, yes? But how else could we express it?
Well, we know that the area of the major rectangle is 100, yes? And we can create an expression for each of the other sub-rectangles, yes? Could we set up an expression to calculate the lower-left sub-rectangle IN TERMS OF the other rectangles?
Hopefully your answer is yes, and hopefully you can apply this same strategy to #53.
Dear Orderly at 29 - Yup you're right, although the book's answer is still correct. Polynomial expressions CAN be written in any order... when you are working with MULTIPLE expressions it is considered "best practice" to order them in descending order of degree.
Dear $th degree, Beyond trinomial, we just say 4th degree, 5th degree, etc. Be patient, Calculus awaits!
Dear MCQ #25 - Go back to the definition of "monomial" in the text. You may need to go back to the definition of whole number.
Dear MCQ #29, 6 is an even number, so the NEXT2 are 8 and 10, so (8)(10) is an expression... can you simplify it? 24 is an even number, so the NEXT2 are 26 and 28, so (26)(28) is an expression... can you simplify it? According to #29, 'n' is an even number, so the NEXT2 are ? and ?, so (?)(?) is an expression... can you simplify it?
Oh, I see, a monomial can only have whole number exponents.
For #29, would the expression to be simplified be (n+2)(n+4)?
And also, for #26, would a good way to begin be to make an expression (x+3)(x+6)-(x-2)(x-4), and then simplify each polynomial, then subtract them from eachother? The book does not give the answer, so is the right answer 15x+10?
In the diagram, the BLUE square (aka the lower-left sub-rectangle) is "labeled" (a-b)^2. That simply means that the BLUE square has sides of length (a-b), yes? I think you are reading too much into the word "labeled" - am I right?
SO, ONE WAY to write a simplified expression for the the BLUE square would be to simplify the expression (a-b)^2, yes?
ANOTHER WAY (aka a second expression) would be to find the area of the whole schmeggegy (aka a^2) and then subtract the areas of the other 3 sub-schmeggegies, leaving you with (hopefully) the same simplified expression you arrived at in method 1.
i have no idea where to start for number 53
ReplyDelete"Good, that's why I assigned it," he said with a snicker!!
ReplyDeleteCan you see that the area of the big square is a*a or a^2?
I'll let that be the only hint for now... lmk if that helped.
bwa ha ha!!
"I will also take a look," she said calmly.
ReplyDelete:D
The book says #29 should be 100-y^2, but shouldn't it be -y^2+100? Because then it would be in order of degree?
ReplyDeleteI'm also having trouble with #53.. Your hint didn't help at all.. ;) The wording troubles me, I don't understand what I am supposed to do. "Write a second expression for the area of the square labeled (a-b)^2"? I understand how you get the area, a^2, from looking at the sides.
ReplyDeleteHelp!!
If the degree of a polynomial goes over four, would it just be a fourth degree binomial or a fifth degree trinomial? or something like that?
ReplyDeleteIf the equation was something like 24x^4 + 8x^2, would you be able to reduce it to something like
ReplyDelete3x^4 + x^2 by dividing both monomials by 8 or would that not be the same?
For #25, on the Mid-Chapter Quiz, I have a feeling it is yes, but seeing we have not done any negative monomial/polynomial work I also have a feeling that it is no.. But if all of the exponents were negative then yes the degree could as well be negative!
ReplyDeleteI don't understand the wording of #29..
ReplyDeleteDear Calm, Cool, and 53,
ReplyDeleteDraw yourself a separate area model depicting (6+4)(7+3). Put 6 and +4 as the length (bottom) and put 7 and 3 as the width (aka height on the left).
Clearly, the area of the lower left sub-rectangle is 6*12=72, yes? But how else could we express it?
Well, we know that the area of the major rectangle is 100, yes? And we can create an expression for each of the other sub-rectangles, yes? Could we set up an expression to calculate the lower-left sub-rectangle IN TERMS OF the other rectangles?
Hopefully your answer is yes, and hopefully you can apply this same strategy to #53.
Dear Orderly at 29 - Yup you're right, although the book's answer is still correct. Polynomial expressions CAN be written in any order... when you are working with MULTIPLE expressions it is considered "best practice" to order them in descending order of degree.
Dear $th degree,
Beyond trinomial, we just say 4th degree, 5th degree, etc. Be patient, Calculus awaits!
Dear MCQ #25 - Go back to the definition of "monomial" in the text. You may need to go back to the definition of whole number.
Dear MCQ #29, 6 is an even number, so the NEXT2 are 8 and 10, so (8)(10) is an expression... can you simplify it? 24 is an even number, so the NEXT2 are 26 and 28, so (26)(28) is an expression... can you simplify it? According to #29, 'n' is an even number, so the NEXT2 are ? and ?, so (?)(?) is an expression... can you simplify it?
For #53, yes, I understand, everything but the 6*12=72.. Where did you get that from? My lower left is 4*3=12.
ReplyDeleteOh, I see, a monomial can only have whole number exponents.
ReplyDeleteFor #29, would the expression to be simplified be (n+2)(n+4)?
And also, for #26, would a good way to begin be to make an expression (x+3)(x+6)-(x-2)(x-4), and then simplify each polynomial, then subtract them from eachother? The book does not give the answer, so is the right answer 15x+10?
For #29 I got n^2+6n+8, is that correct?
ReplyDeleteOOPS, yes, I switched examples mid-stream and left a typo behind... thanks for checking!
ReplyDeleteFor #29, (n+2)(n+4) is a correct FACTORED expression... n^2+6n+8 is THE correct SIMPLIFIED expression.
For #26... YUP!
Assuming you gotsk #53, by jove, I think you've GOT IT ALL... Well done!!!
But I still don't gotsk #53.. =(
ReplyDeleteI don't understand what they mean by "labeled (a-b)^2". If they are telling you to label your expression (a-b)^2 what does it mean?
In the diagram, the BLUE square (aka the lower-left sub-rectangle) is "labeled" (a-b)^2. That simply means that the BLUE square has sides of length (a-b), yes? I think you are reading too much into the word "labeled" - am I right?
ReplyDeleteSO, ONE WAY to write a simplified expression for the the BLUE square would be to simplify the expression (a-b)^2, yes?
ANOTHER WAY (aka a second expression) would be to find the area of the whole schmeggegy (aka a^2) and then subtract the areas of the other 3 sub-schmeggegies, leaving you with (hopefully) the same simplified expression you arrived at in method 1.
GOTSK IT NOW??!!
OOOHHH Yes I gotsk it! I just didn't understand the wording! =)
ReplyDeleteThe book says some weird answers.. Would a correct answer be a^2-b^2-2ab?
ReplyDeleteDear Weirdo,
ReplyDelete(a-b)^2 = a^2 - 2ab - b^2
... does that answer your question?
...Yes!
ReplyDelete