Question

Factor completely: 4x
2
(x
2
+7)−(x
2
+7)

Answer 1

Factor out the common factor (x^2 + 7):

4x^2(x^2 + 7) − (x^2 + 7) = (x^2 + 7)(4x^2 − 1).

Then factor 4x^2 − 1 as a difference of squares:

4x^2 − 1 = (2x − 1)(2x + 1).

So the full factorization is (x^2 + 7)(2x − 1)(2x + 1).