How do you factor #3.375v^3+15.625r^6#?

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Answer 1 · 2015-04-21T17:55:21

Prime factorise 3375 and 15625

3375=333555=#3^3*5^3# and 15625= 555555=# 5^3*5^3#

#3.375v^3 +15.625r^6= (3^3*5^3* v^3 )/10^3 +( 5^3*5^3)/10^3 (r^2)^3#

=# (5^3/10^3) [3^3 v^3 +5^3 (r^2)^3]#

=#(5^3/10^3)[(3v)^3 +(5r^2)^3]#

=#(5/10)^3 (3v+5r^2)(9v^2 -15vr^2 +25r^4)#

=#1/8(3v+5r^2)(9v^2 -15vr^2 +25r^4)#