What is factor 4^{n+2}+2^{2n+2} ?

The solution to factor 4^{n+2}+2^{2n+2} is 5*4^{1+n}

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factor 4^{n+2}+2^{2n+2}

factor

4^{n + 2} + 2^{2 n + 2}

5 \cdot 4^{1 + n}

Solution steps

4^{n + 2} + 2^{2 n + 2}

Factor

2 n + 2 : 2 (n + 1)

= 4^{n + 2} + 2^{2 (n + 1)}

2^{2 (n + 1)} = 4^{n + 1}

= 4^{n + 2} + 4^{n + 1}

Apply exponent rule:

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

= 4^{2} \cdot 4^{n} + 4^{1} \cdot 4^{n}

Rewrite as

= 4 \cdot 4 \cdot 4^{n} + 1 \cdot 4 \cdot 4^{n}

Factor out common term

4 \cdot 4^{n}

= 4 \cdot 4^{n} (4 + 1)

Refine

= 5 \cdot 4^{n + 1}

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What is factor 4^{n+2}+2^{2n+2} ?
The solution to factor 4^{n+2}+2^{2n+2} is 5*4^{1+n}