How do you factor completely #10r^3s^2 + 25r^2s^2 – 15r^2s^3#?

1 Answer
George C.
May 15, 2017

#10r^3s^2+25r^2s^2-15r^2s^3 = 5r^2s^2(2r+5-3s)#

Explanation:

Given:

#10r^3s^2+25r^2s^2-15r^2s^3#

Note that all of the terms are divisible by #5#, #r^2# and #s^2#, so by #5r^2s^2#.

So we can separate that out as a factor:

#10r^3s^2+25r^2s^2-15r^2s^3 = 5r^2s^2(2r+5-3s)#

The remaining factor is already linear, so will not factor any further.

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