Factorise the following.
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1. 16a^2 - 25b^2
= (4a)^2 - (5b)^2
= (4a + 5b) (4a - 5b)
2. 2x - 32x^5
= 2x ( 1 - 16x^4)
= 2x { (1)^2 - (4x^2)^2}
= 2x ( 1 + 4x^2 ) ( 1 - 4x^2)
= 2x ( 1 + 4x^2 ) { (1)^2 - (2x)^2 }
= 2x ( 1 + 4x^2 ) ( 1 + 2x ) ( 1 - 2x)
3. (2x + 3y)^2 - 16z^2
= (2x + 3y)^2 - (4z)^2
= (2x + 3y + 4z) (2x + 3y - 4z)
4. a(2a + 3b)^2 - 4(3a - 4b)^2
= a ( 4a^2 + 12ab + 9b^2) - 4 ( 9a^2 - 24ab + 16b^2)
= 4a^3 + 12a^2b + 9ab^2 - 36a^2 - 96ab + 64b^2
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