Question 766739
<pre>
Hi,

Most of your problems can be solved using the following 3 identities:
1) {{{a^3 - b^3 = (a - b)*(a^2 + a*b + b^2)}}}
2) {{{a^3 + b^3 = (a + b)*(a^2 - a*b + b^2)}}}
3) {{{a^2 - b^2 = (a + b)*(a - b)}}}

I'm solving a few below - go through these and try the rest yourself.

1) {{{125*x^3 + 64}}}
= {{{(5*x)^3 + 4^3}}}     => Now it is of the form a^3 + b^3

= {{{(5*x + 4)*(25*x^2 - 20*x + 16)}}}  --> Using identity (2)

Choice D

2) 
{{{27*x^3 - 8}}}
= {{{(3*x)^3 - 2^3}}} => Now it is of the form a^3 - b^3
= {{{(3*x - 2)*(9*x^2 + 6*x + 4)}}}  ---> Using identity (1)

Choice E

3) 
{{{a^4 - 64}}}
= {{{(a^2)^2 - 8^2}}} => Now it is of the form a^2 - b^2
= {{{(a^2 + 8)*(a^2 - 8)}}}    ---> Using identity (3)
Choice B

4)
{{{-2*w^4 + 1250}}}  ---> take out the common factor of -2
= {{{-2*(w^4 - 625)}}}
= {{{-2*((w^2)^2 - 25^2)}}} => Now it is of the form a^2 - b^2
= {{{-2*(w^2 + 25)*(w^2 - 25)}}}    ---> Using identity (3)
= {{{-2*(w+5)*(w-5)*(w^2 + 25)}}}   ---> since w^2 - 25 is also of the form a^2 - b^2
Choice E

Hope you get the idea now :)



</pre>