Explain conversion logic in three examples

[Glebiys]

Hello,

First example. How was this conversion done?



Second example



Could you guide me on the right path?

I would be glad if you explain these transformations step by step and tell you which formulas to use. (As I understand it - the difference of squares, the square of the difference).

Thank you!
Best regards,
Alex

 

[mmm4444bot]

Hello Glebiys. There are two methods, often called the "Product/Sum Method" and "Factor by Grouping Method" (also known as decomposition).

Search for examples using those method names.

You can also go to youtube and search for ZQ-NRsWhOGI (sorry I can't post a workable link), to watch some examples explained.

Let us know if you have any questions about what you find.

?

 

[JeffM]

I am very confused by your question.

How in the world can expect to understand limits (usually studied in the first semester of calculus) if you do not know how to factor a quadratic (usually studied in first year algebra)?

 

[HallsofIvy]

Hello,

First example. How was this conversion done?

View attachment 28916

Second example

View attachment 28917

Could you guide me on the right path?

I would be glad if you explain these transformations step by step and tell you which formulas to use. (As I understand it - the difference of squares, the square of the difference).

Thank you!
Best regards,
Alex

Hello,

First example. How was this conversion done?

View attachment 28916

Second example

View attachment 28917

Could you guide me on the right path?

I would be glad if you explain these transformations step by step and tell you which formulas to use. (As I understand it - the difference of squares, the square of the difference).

Thank you!
Best regards,
Alex

I am not sure what "conversion" you are talking about. One of the things you must have learned in an algebra class is that (x- a)(x- b)= x(x- b)- a(x- b)= x^2- bx- ax+ ab= x^2- (a+b)x+ ab. In particular, if b= a that is (x- a)(x- a)= (x- a)^2= x^3- (a+ a)x+ a^2= x^2- 2ax+ a^2 and if b= -a that is (x- a)(x+ a)= x^2- (a- a)x+ a(-a)= x^2- a^2

Once you know that, looking at x^2- 4, and comparing to the ones above, you should see that this has a= 2, b= -2. x^2- 4= (x- 2)(x+ 2).
Similarly comparing x^2- 4x+ 4 is of the form x^2- 2ax+ a^2 with a= 2. So x^2- 4x+ 4.

So $\displaystyle \frac{x^2- 4}{x^2- 4x+ 4}= \frac{(x- 2)(x+ 2)}{(x- 2)^2}$.

 

[Deleted member 4993]

Hello,

First example. How was this conversion done?

View attachment 28916

Second example

View attachment 28917

Could you guide me on the right path?

I would be glad if you explain these transformations step by step and tell you which formulas to use. (As I understand it - the difference of squares, the square of the difference).

Thank you!
Best regards,
Alex

Do you know

How to. FACTORIZE quadratic equation s?

If not, Google that topic.

If you still have questions - please come back and ask.

Quadratic equations are essential in Calculus. You must "master" those to grapple with Calculus.