MHB Is my factoring correct for these polynomials?

[mathdad]

Factor each polynomial given.

(A) u^2v^2 - 225

(B) 81x^4 - x^2

For (A), I got (uv - 15)(uv + 15). Is this right?

Solution for (B):

x^2(81x^2 - 1)

I think the binomial inside the parentheses can be factored.

So, (81x^2 - 1) becomes (9x - 1)(9x + 1).

My answer for (B) is x^2(9x - 1)(9x + 1).

Is this correct?

 

[joypav]

Both are correct.
These are both problems testing your knowledge of factoring values that are "perfect squares".
Meaning,
a^2 - b^2 = (a+b)(a-b) For example,
in (a) you have u^2v^2 - 225. Using the formula, a=uv and b=15. So your answer is (a+b)(a-b)=(uv+15)(uv-15).

 

[kaliprasad]

Both are correct.
These are both problems testing your knowledge of factoring values that are "perfect squares".

Not perfect squares but difference of perfect squares

 

[mathdad]

It feels awesome to get the right answer.