What is factor 3^{x+y}+3^{x-y} ?

The solution to factor 3^{x+y}+3^{x-y} is 3^{x-y}(3^{2y}+1)

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factor 3^{x+y}+3^{x-y}

factor

3^{x + y} + 3^{x - y}

3^{x - y} (3^{2 y} + 1)

Solution steps

3^{x + y} + 3^{x - y}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

3^{x + y} = 3^{x} \cdot 3^{y}

= 3^{x} \cdot 3^{y} + 3^{x - y}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

3^{x - y} = 3^{x} \cdot 3^{- y}

= 3^{x} \cdot 3^{y} + 3^{x} \cdot 3^{- y}

Factor out common term

3^{x} \cdot 3^{- y} : 3^{x} \cdot 3^{- y} (3^{2 y} + 1)

= 3^{x} \cdot 3^{- y} (3^{2 y} + 1)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3^{x} \cdot 3^{- y} = 3^{x - y}

= 3^{x - y} (3^{2 y} + 1)

a^{4} + 64

(5 x - 9)^{4}

6 x - 4 y - x^{2} - 2 y^{2}

40 + 32 + (6 x^{8})

3 j^{112} + 3 j^{39}

What is factor 3^{x+y}+3^{x-y} ?
The solution to factor 3^{x+y}+3^{x-y} is 3^{x-y}(3^{2y}+1)