Question 1757
1. Given {{{x^2 - 4y^2}}}, this factorises to {{{(x+2y)(x-2y)}}}. So similarly, {{{(a-b)^2 - 4(c-d)^2}}} becomess {{{((a-b)+2(c-d))((a-b)-2(c-d))}}}

2. think of {{{6z^2 + 23z - 4}}}. This factorises to {{{(6z-1)(z+4)}}}...you just have to mess around with the possibilities and eventually find the correct pairing. There is no "secret" here, just looking at the numbers.

Hence, we then get {{{ (6(x-y)-1)(x-y+4) }}}

3. {{{(5x^9)/4}}}

4. {{{m^(-6)}}} becomes {{{1/m^6}}}

5. {{{(2a^(-3))^2}}} becomes {{{4a^(-6)}}} which becomes {{{4/a^6}}}

cheers
Jon.