Verwandle in ein Produkt!

Question

Aufgabe: Verwandle in ein Produkt!
a. 12t + 3t² = 
b. 56y² - 2yx = 
c. t² - 25t =

My German uncle asked me for guidance to help his grandson solving these math problems. I cant remember the method for this type of task. I hope some one here could help me explain.

Both German and english is fine  
------------------------------------------------------------------------
Mein deutscher Onkel bat mich um Anleitung, um seinem Enkel bei der Lösung dieser mathematischen Probleme zu helfen. Ich kann mich nicht an die Methode für diese Art von Aufgabe erinnern. Ich hoffe, jemand hier konnte mir helfen, es zu erklären.

Answer 1

Hallo

Immer sehen , was man ausklammern kann,  a)t*(...) ; b)  2y*(...)  c)  like a ) but then a^2-b^2=(a+b)*c+d)

Gruß lul

Comments

Vielen dank für den Anwort

Answer 2

Aloha :)

$$12t+3t^2=3t\cdot4+3t\cdot t=3t\cdot(4+t)$$$$56y^2-2yx=2y\cdot28y-2y\cdot x=2y\cdot(28y-x)$$$$t^2-25t=t\cdot t-t\cdot 25=t\cdot(t-25)$$

Comments

Vielen dank für den Anwort. Es war ein grosse hilfe für mich.

Answer 3

Hi emmf0703,

you just can fracture out some variables and numbers:

a) 12t + 3t^2 = 3t(4+t)

b) 56y^2 -2yx = 2y(28y-x)

c) t^2-25t = t(t-25)

Comments

Thank you very much It was a good help.

I have another question while I would have to explain the method for these tasks to the german schoolkid.

In which situations/cases do we use this method  of fractureing out as many variables and numbers?

---

You’re welcome!

So, there are many cases in which it is useful to transform a sum in a product:

Assuming the child goes to a lower grade, it probably might be a good example to explain that using the distributive law can help to simplify fractions: It is not possible to simplify a fracture with sums, but if you transform that into a product, it‘ll be possible.

E. g. $$ \frac{4t+6t^2}{2at^2} = \frac{2t(2+3t)}{2at^2} = \frac{2+3t}{at} $$