What is factor 3^{2x}+3^x-756 ?

The solution to factor 3^{2x}+3^x-756 is (3^x-27)(3^x+28)

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factor 3^{2x}+3^x-756

factor

3^{2 x} + 3^{x} - 756

(3^{x} - 27) (3^{x} + 28)

Solution steps

3^{2 x} + 3^{x} - 756

Apply exponent rule:

a^{b c} = (a^{b})^{c}

3^{2 x} = (3^{x})^{2}

= (3^{x})^{2} + 3^{x} - 756

Break the expression into groups

= ((3^{x})^{2} - 27 3^{x}) + (28 3^{x} - 756)

Factor out

3^{x}

from

(3^{x})^{2} - 27 3^{x} : 3^{x} (3^{x} - 27)

Factor out

28

from

28 3^{x} - 756 : 28 (3^{x} - 27)

= 3^{x} (3^{x} - 27) + 28 (3^{x} - 27)

Factor out common term

3^{x} - 27

= (3^{x} - 27) (3^{x} + 28)

\frac{1}{3} - \frac{2}{5} + \frac{1}{7}

k^{2} + 14 k + 45 = 0

\frac{- 10 + - 40}{2}

x^{2} + 11 x + 28 > 0

\frac{x}{3} - \frac{x}{2} = 5

What is factor 3^{2x}+3^x-756 ?
The solution to factor 3^{2x}+3^x-756 is (3^x-27)(3^x+28)