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


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*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 ! 

*

*$$9x^4 - 9x^2y^2 - 4x^2 + 4y^2$$
Group in paris such that; $9x^2(x^2-y^2) - 4(x^2 - y^2) = (x^2 - y^2)(9x^2 - 4)$
Then using the difference of 2 squares we get: $$(x-y)(x+y)(3x-2)(3x+2)$$


2.$3x^2 + 11x - 20$, factorise to $(x-5)(3x-4)$. As @mathlove pointed out $11(a-b) - 20 + 3(?)^2$, where $ ? = a-b$. Which is similar to the previous equation. So utilising it's result we get it factorised down to $(a-b-5)(3(a-b-4)$


*$78^2 + 312 + 4 = 78^2 + 316$, using the fact that $(a + b)^2 = a^2 + 2ab + b^2$, we get $(70 + 8)^2 + 316 = (4900 + 1120 + 64) + 316 = 6400$

*Apply the same reasoning as number 3
