What is factor 9b^{2x}-1/4 ?

The solution to factor 9b^{2x}-1/4 is (3b^x+1/2)(3b^x-1/2)

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factor 9b^{2x}-1/4

factor

9 b^{2 x} - \frac{1}{4}

(3 b^{x} + \frac{1}{2}) (3 b^{x} - \frac{1}{2})

Solution steps

9 b^{2 x} - \frac{1}{4}

Rewrite

9 b^{2 x}

(3 b^{1 x})^{2}

= (3 b^{1 \cdot x})^{2} - \frac{1}{4}

Apply radical rule:

a = (a)^{2}

\frac{1}{4} = (\frac{1}{4})^{2}

= (3 b^{1 x})^{2} - (\frac{1}{4})^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(3 b^{1 x})^{2} - (\frac{1}{4})^{2} = (3 b^{1 x} + \frac{1}{4}) (3 b^{1 x} - \frac{1}{4})

= (3 b^{1 x} + \frac{1}{4}) (3 b^{1 x} - \frac{1}{4})

Refine

= (3 b^{x} + \frac{1}{2}) (3 b^{x} - \frac{1}{2})

e^{2 + 2 i}

[(x + 8) - y]^{2}

x (a + b - c) - (- y (a + b - c))

21 b + 63 b

[x^{2}]

What is factor 9b^{2x}-1/4 ?
The solution to factor 9b^{2x}-1/4 is (3b^x+1/2)(3b^x-1/2)