November 16, 2010

Difference of Two Squares (CA SS: 11.0)

Here is our factoring algorithm:

Remove the Greatest Monomial Factor
Check for the Difference of Two Squares
Check for a Perfect Square Trinomial
Factor x2+bx+c
Factor ax2+bx+c
Factor by Grouping
ALWAYS FACTOR COMPLETELY!



a2 - b2 = (a + b)(a - b)

p.268 (9-17:odd,39,41,47,49,51)
Per. 4: p.268 (21,41,61,63,73,77,79,81)

24 comments:

jose c per3 said...

do we have 2 justify

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Kent Y. Period 4 said...

Journal entry: 11/16/10

Today in math, I learned how to check for the difference of two squares. To do this, you must know many of the perfect squares, such as 1*1=1, 2*2=4, 3*3=9, 4*4=16, 5*5=25, e.t.c. Also you must check if it's the DIFFERENCE of two perfect squares. Here are some examples:

x^2-25 is a difference of two squares since x^2 can be divided equally, x*x and 25 can be divided equally to 5.

Next you must do the opposite of what we learned in Chapter 5, x^2-25=(x+5)(x-5). Sometimes you might have to go back to step 1 of the algorithm factor, like 4x^4-64=4(x^4+16)=4(x^2+4)(x^2-4)=4(x^2+4)(x+2)(x-2).

Anonymous said...

Journal 11/16/2010

Today we learned about the differecne of squares. In order to compare difference of square, we had to check if the two terms have a difference sign(-), and two perfect squares.Not only that, we had to be careful if they can become positive or negetive sign using communicative property like this one: (-49+16a squared = 16a squared -49)

RachelC Per.5 said...

11/16/10 In class today we refreshed our memories of perfect squares and the difference of two squares. We also went over how negative integers can never be perfect squares because for a number to be a perfect square, it's factors must be identical to each other. Ex.-49 is not a perfect square because its factors are 7,-7, and those numbers are not identical like 49's factors are: 7,7, those are identical, so 49 is a perfect square. We also started using the "factoring algorithms" rules. Ex. 32y^2-8y^6=8y^2(4-y^4)<---steps one and two =8y^2(2+y^2)(2-y^2)

April said...

Journal Entry Nov 11, 2010
Today I learned that to check the difference of two squares, you have to check what number can multiply itself to make that factor. well for an example: x2-25... the difference of two squares is (x*x)(5*5) to find the answer you have to use the distributive property...(x+5)(x-5)

April said...

Oh wait I put the wrong date I did it today though... got mixed up sorry

Unknown said...
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Unknown said...

Journal entry: 11-16-10

Today, we learned how to identify, then factor the difference of two squares. At first, if the polynomial is not a difference of two squares, you could still factor completely. First, you just factor the polynomial. Then, you can get the polynomials in between the two (these things) and factor them. This is how you factor completely.

Kevin Kang Period 4

Anonymous said...

Today we discussed the second step of the Factoring Algorithm; check for the differences of two squares. First we checked if the expression was the difference of two squares. X to the second power -25 is but x to the second power -24 isn't. -49+16a to the second power is because if you use the commutative property then you get 16a to the second power -49. We also used a to the second power -b to the second power = (a+b)(a-b).
Examples:
4y to the second power -49=(2y+7)(2y-7)
16x to the second power -25y to the second power =(4x+5y)(4x-5y)
32y to the second power -8y to the sixth power =8y to the second power (4-y to the fourth power)
=8y to the second power (2+y to the second power)(2-y to the second power)

Anonymous said...

Today we discussed the second step of the Factoring Algorithm; check for the differences of two squares. First we checked if the expression was the difference of two squares. X to the second power -25 is but x to the second power -24 isn't. -49+16a to the second power is because if you use the commutative property then you get 16a to the second power -49. We also used a to the second power -b to the second power = (a+b)(a-b).
Examples:
4y to the second power -49=(2y+7)(2y-7)
16x to the second power -25y to the second power =(4x+5y)(4x-5y)
32y to the second power -8y to the sixth power =8y to the second power (4-y to the fourth power)
=8y to the second power (2+y to the second power)(2-y to the second power)

Eric X. Per. 3 TA said...

Period 2: April H.
Period 3:
Period 4: Kent Y. & Kevin K.
Period 5: Michelle M. & Rachel C.
Period 6: Katie K.


Also, Club Challenge #2 is tomorrow! :)

Eric X. Per. 3 TA said...

Oh, an Mr. Gerson, there is an error in the blog entry.

Gilbert Z. Per. 2 said...

what is the hw because it doesn't come up on my computer.

Natasha L Per.4 TA said...

Yay happy mathcounts tomorrow ^^ Student council is tomorrow too >.> dang

Anonymous said...

Today in class, we had a lesson about the difference of two squares.
You have to follow these patterns, a^2+b^2=(a+b)(a-b) in order to get the answer.For example:
x^2-25 to the second power, check to see the difference of two squares
x*x is x to the second power and
5*5 is 25
another example:
-49+16a^2 you could use the communicative property by flipping it around 16a^2-49 the difference of two squares would be 4a*4a and 7*7,so 16a^2-49=(4a+7)(4a-7)

Anonymous said...

Journal Entry for 11/16/2010.

Today in class,we reviewed the second step of Factoring Algorithms, which was to find the difference of two squares. Before you do this, however, you should know the basic perfect squares, such as 1 (1*1), 4 (2*2), 9 (3*3), 16 (4*4), 25 (5*5), 36 (6*6), and so on. Once you know those, this lesson would be easy. But keep in mind, negative integers can NEVER be a perfect square. Why? Because in order for a number to be a perfect square, it must have IDENTICAL to each other. For example, -25 cannot be a perfect square because -5 and 5 aren't identical. However, if it were 25 (5, 5) that would be a perfect square.

Natasha L Per.4 TA said...

Period 2: April H.
Period 3: Diana K.
Period 4: Kent Y. & Kevin K.
Period 5: Michelle M. & Rachel C.
Period 6: Katie K. & Trisha L.

MakaylaLPeriod2* said...

Journal entry:
November 16,2010

In math today, I learned how to determine whether or not an equation is a perfect square or not. ie:
a)x^2-25 Perfect Square
b)x^2-24 NOT a Perfect Square
Explaination:
x^2-25 is a perfect square because 5 to the power of 2 is 25, when nothing to the power of 2 equals 24.

Natasha L Per.4 TA said...

Period 2: April H. & Makayla L.
Period 3: Diana K.
Period 4: Kent Y. & Kevin K.
Period 5: Michelle M. & Rachel C.
Period 6: Katie K. & Trisha L.

GiselleBPer2 said...

@ Gilbert
Homework is:
pg. 268(9-17 odd,39,41,47,49,and 51)

Mr. Gerson said...

@Eric, thanks. I fixed it. I was hoping someone other than a TA would have caught it, but it was after 5PM when you announced it. Nobody noticed.

Remember: the sum of two squares is never factorable.