how do I factor these equations?

Question

4(b+3a)^2 - 9(b^2 + 3a)^2

and

x^4 - y^4 + 5x^2 - 5y^2

Answer 1

First simplify the first formula

4(b + 3a)^2 - 9(b^2 + 3a)^2
= 4(b^2 + 6ab + 9a^2) - 9(b^4 + 6ab^2 + 9a^2)
= 4b^2 + 24ab + 36a^2 - 9b^4 + 54ab^2 + 81a^2
= 117 a^2 + (24 b + 54 b^2) a + (-9 b^4 + 4 b^2)

It does not seem that you can factor much about this.

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x^4 - y^4 + 5x^2 - 5y^2 = (x^2 - y^2) (x^2 + y^2 + 5)

Answer 2

4(b+3a)^2-9(b^2+3a)^2
=[2(b+3a)]^2-[3(b^2+3a)^2]
use the formula of difference of squares
=[2(b+3a)+3(b^2+3a)][2(b+3a)-3(b^2+3a)]

x^4-y^4=(x^2+y^2)(x^2-y^2)
5x^2-5y^2=5(x^2-y^2)
now the expression
(x^2+y^2)(x^2-y^2)+5(x^2-y^2)
taking out (x^2-y^2)
(x^2-y^2)(x^2+y^2+5)
=>(x+y)(x-y)(x^2+y^2+5)

Answer 3

Use this mnemonic. PEMDAS
This website should help.
http://www.mathgoodies.com/lessons/vol7/order_operations.html