How to factor when no common factors?

[Gringo123]

How can I foctorise / factor this given that 25 and 49 share no common factors?

25x² - 49y²

 

[Mentallic]

Note that 25=5² and $$a^nb^n=(ab)^n$$

 

[Mark44]

How can I foctorise / factor this given that 25 and 49 share no common factors?

25x² - 49y²

This is a difference of squares.

 

[iRaid]

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

Make sure to make a and b not squared..So instead of 25, 5.

 

[Mentallic]

given that 25 and 49 share no common factors?

Neither do x² and y² share any common factors, so this should imply you're looking for another factoring method other than finding a common factor. In this case, difference of two squares.

 

[Gringo123]

Thanks everyone. So am I right in saying that the answer would be:
(5x - 7y) (5x + 7y)
?

 

[Mentallic]

Rather than asking for confirmation from us, why don't you expand your answer to check it?

 

[iRaid]

Thanks everyone. So am I right in saying that the answer would be:
(5x - 7y) (5x + 7y)
?

That would be correct.

 

[Gringo123]

Thanks Raid!

 

[Mentallic]

If you prefer the easier way out (and the lazy approach at that), that's up to you, but you should reconsider becoming more trusting in yourself and not always of those around you.

In this problem, if you expanded your answer it will confirm whether you factorized correctly or not. In other topics you have been studying, for example the quadratic factoring, if asked to solve

$$x^2-x-6=0$$ and you factorize it as so $$(x-3)(x+2)$$ you can check by expanding, or even plug your values x=3 and x=-2 into the quadratic to see if it's correct.

I'm just saying that there are ways to check your work so you become more independent with your mathematics. Having low confidence in your answers would be bad in tests, considering you're all alone in those situations.