Question 189972
factor 

1.) 

{{{ 27f^3+64 }}}
=> {{{ (3f)^3 + (4)^3 }}}

(we will use the formula for {{{ a^3 + b^3 = (a + b)(a^2 - ab + b^2) }}} )

=> {{{ (3f + 4)((3f)^2 - (3f)*(4) + (4)^2) }}}
=> {{{ highlight((3f + 4)(9f^2 - 12f + 16)) }}}

2.) 

{{{ 2x^3+6x^2+x+3 }}}  (now, we group the first two terms and the last two terms, and take out the common factors from each of them) 

=> {{{ 2x^2*(x+3) + 1*(x+3) }}}
=> {{{ highlight((x+3)(2x^2 + 1)) }}}

3.)

{{{ 8m^3-125 }}}  (this can be expressed as perfect cubes of 2m and 5)
=> {{{ (2m)^3 - (5)^3 }}}
=> {{{ (2m - 5)((2m)^2 + (2m)*(5) + (5)^2) }}}
(we have used the formula for {{{ a^3 - b^3 = (a - b)(a^2 + ab + b^2) }}} )
=> {{{ highlight((2m - 5)(4m^2 - 10m + 25)) }}}

Hope this helps you.