How do you factor 40v^3-625?

2 Answers
Jun 2, 2015

40=5*8
and 625=5*125
So 40v^3-625=5*(8v^3)+5*(-125)
40v^3-625=5(8v^3-125)

Jun 2, 2015

40v^3-625

=5(8v^3-125)

=5((2v)^3-5^3)

=5((2v)-5)((2v)^2+(2v)5+5^2)

=5(2v-5)(4v^2+10v+25)

...using the difference of cubes identity:

a^3-b^3 = (a-b)(a^2+ab+b^2)