Expansion and factorisation I have a little problems with a few questions here and I need help.. Thanks ...


*

*Factorise completely 


$$9x^4 - 4x^2 - 9x^2y^2 + 4y^2 $$
My workings ..
$$ (3x^2+2x)(3x^2-2x) - y^2 (9x^2-4) = (3x^2 + 2x)(3x^2 -2x) - y^2 (3x+2)(3x-2) $$


*Factorise $3x^2 + 11x - 20$ and , hence Factorise completely 


$$11a - 11b - 20 + 3a^2 + 3b^2 - 6ab$$
My workings ...
$$ 11(a-b) - 20 + (3a-3b)(a-b)$$


*Evaluate the following by algebraic expansion of factorisation 


(A) $78^2 + 312 + 4$
(B) $501^2 - 1002 + 1$ 
Thanks a lot ! 

HINTS : 
For 1.
The coefficients are $\pm 9,\pm 4$, so
$$9x^4-4x^2-9x^2y^2+4y^2=(9x^4-9x^2y^2)-(4x^2-4y^2)$$
is worth trying.
For 2.
Compare $3x^2+11x-20$ with $$11a-11b-20+3a^2+3b^2-6ab=11(a-b)-20+3(?)=3(?)+11(a-b)-20$$
For 3.
Note that $312=78\times 4$ and that $1002=2\times 501$.
