How would I factor these two polynomials?

a) 36x^6-25y^4
b) 4x^6y^4-28x^3y^2+49

Question

How would I factor these two polynomials?

a) 36x^6-25y^4
b) 4x^6y^4-28x^3y^2+49

anonymous · Answer

a) $$36x ^{6}-25y ^{4}$$
b) $$4x^6y^4-28x^3y^2+49$$

directrix · Answer

@rach_ell

Try the difference of two squares factoring pattern on this one:

36x^6-25y^4

anonymous · Answer

I attempted to before, but just wasn't sure what to make of the exponent 6. Usually when it's x^2 or x^4, it's just x or x^2 (respectively) in each bracket .

directrix · Answer

How about this:

36x^6-25y^4 = (6x³)²  - (5y²)²   -> Do you see this as the difference of two squares?

@rach_ell

directrix · Answer

(6x³)² - (5y²)² =

anonymous · Answer

Would it be like this? (6x³)² - (5y²)² = (6x^3-5y^2)(6x+5y^2)

directrix · Answer

Correct.

directrix · Answer

The second problem looks like a perfect square trinomial scenario.

directrix · Answer

Reminder attached.

directrix · Answer

@rach_ell

anonymous · Answer

Okay, I got this:

$$4x^6y^4-28x^3y^2+49 $$
= $$(2x^3y^2)^2-28x^3y^2+49$$
= $$(2x^3y^2-7)(2x^3y^2+7)$$

anonymous · Answer

oops, I mean (2x^3y^2-7)^2

directrix · Answer

Do you see the bad sign here?  See attachment.

directrix · Answer

I agree with this -->   (2x^3y^2-7)^2

directrix · Answer

@rach_ell

anonymous · Answer

Yes, I realized the mistake after I checked a second time. Thank you so much for helping!

directrix · Answer

You are welcome.