Question

(4x^2 + 4x + 4)(4x^2 -4x + 4) = 4(x^2 + x + 1) * 4(x^2 -x + 1) right?

Answer 1

right.

Answer 2

ya its right

Answer 3

Those are equivalent, yes. You can further expand it, though. Easiest way imho is long multiplication

Answer 4

yes

Answer 5

Distributive property of multiplication over addition.

Answer 6

@nbouscal is factoring out a 4 out of (4x^2 +4x + 4) the opposite of distributive property?

Answer 7

They're both the distributive property just taken in different directions.