How do you factor #64v^3-125#?

1 Answer
Aug 18, 2016

Answer:

#(4v-5)(16v^2+20v+25)#

Explanation:

This is a #color(blue)"difference of cubes"# and , in general, factorises as.

#color(red)(|bar(ul(color(white)(a/a)color(black)(a^3-b^3=(a-b)(a^2+ab+b^2))color(white)(a/a)|)))........ (A)#

Now #64v^3=(4v)^3" and " 125=(5)^3#

#rArra=4v" and " b=5#

substitute into (A)

#rArr64v^3-125=(4v-5)(16v^2+20v+25)#