factor 4x^2-36 (2x-6)^2. (4x-6)^2(2x+9)(2x-4) (2x+6)(2x-6)

Factor the following:
4 x^2 - 36

Factor 4 out of 4 x^2 - 36:
4 (x^2 - 9)

x^2 - 9 = x^2 - 3^2:
4 (x^2 - 3^2)

Factor the difference of two squares. x^2 - 3^2 = (x - 3) (x + 3):

Answer: 4 (x - 3) (x + 3)
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Factor the following:
(2 x - 6)^2

Factor 2 out of 2 x - 6:
(2 (x - 3))^2

Multiply each exponent in 2 (x - 3) by 2:
2^2 (x - 3)^2

2^2 = 4:

Answer:  4 (x - 3)^2
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Factor the following:
(4 x - 6)^2 (2 x + 9) (2 x - 4)

Factor 2 out of 2 x - 4:
(4 x - 6)^2 2 (x - 2) (2 x + 9)

Factor 2 out of 4 x - 6:
2 (2 (2 x - 3))^2 (2 x + 9) (x - 2)

Multiply each exponent in 2 (2 x - 3) by 2:
2×2^2 (2 x - 3)^2 (2 x + 9) (x - 2)

2^2 = 4:
4×2 (2 x - 3)^2 (2 x + 9) (x - 2)

4×2 = 8:

Answer: 8 (2 x - 3)^2 (2 x + 9) (x - 2)

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Factor the following:
(2 x + 6) (2 x - 6)

Factor 2 out of 2 x - 6:
2 (x - 3) (2 x + 6)

Factor 2 out of 2 x + 6:
2×2 (x + 3) (x - 3)

2×2 = 4:

Answer: 4 (x + 3) (x - 3)