Factor this: 25+36m²-4n²+60m+4n-1 (10 points guaranteed)?

Question

please factor this FULLY, and please show me STEP BY STEP. thank you for your help, i will give best answer 10 points.

Answer 1

Your first step would be to combine the like terms, which in this case is only the "25" and the "-1", so combine them to get 24:

36m²-4n²+60m+4n+24

After that, group together the terms with similar variables:

(36m²+60m)-(4n²+4n+24)

Then factor out each of those polynomials:

12m(3m+5)-4(n²+n+6)

Factor it one more time and you have factored it out as much as possible:

12m(3m+5)-4(n+3)(n-2)

And that should be the answer. However, there may be different answers based upon how you decide to do this. For example, this may also be an answer if you group the 24 with the m's:

12(3m2+5m+2)-4n(n+1)

However, I like the original answer I gave you better.

Answer 2

Several things to notice:

1. There is no "mn" term.
2. The m^2 and n^2 terms are of opposite polarities.
3. The coefficients of m^2 and n^2 are perfect squares.

Without solving this, I'm guessing that what you will need to do is complete the square to get a (am+b)^2-(cn+d)^2, which is a difference of 2 squares, which can be factored.

This may be completely wrong, but if we proceed to get an answer like that:

(36m^2+60m) - (4n^2-4n) +(25-1)
=36*(m^2+5m/3+25/36) - 4*(n^2-n+1/4) + (25-1) - 36*(25/36) + 4*(1/4)
=36*(m+5/6)^2 - 4*(n-1/2)^2 + 24-25+1
=(6m+5)^2 - (2n-1)^2
=(6m+2n+4)*(6m-2n+6)
=4*(3m+n+2)*(3m-n+3)

Answer 3

25+36m²-4n²+60m+4n-1
combine terms
24+36m²-4n²+60m+4n
factor out 4
4(6 + 9m² - n² + 15m + n)

Answer 4

-4nsqrd+4n+36msqrd+60m+25-1
-4n(n-1)+12m(3m+5)+24
divide thru by 4
-n(n-1)+3m(3m+5)+6