What is expand (a^{x+1}+1/2 b^x)^3 ?

The solution to expand (a^{x+1}+1/2 b^x)^3 is (8a^{3(x+1)}+6a^{x+1}b^{2x}+b^{3x}+12b^xa^{2(x+1)})/8

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expand (a^{x+1}+1/2 b^x)^3

expand

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

\frac{8 a ^{3 (x + 1)} + 6 a ^{x + 1} b ^{2 x} + b ^{3 x} + 12 b ^{x} a ^{2 (x + 1)}}{8}

Solution steps

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

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

(a^{x + 1})^{3} + 3 (a^{x + 1})^{2} \frac{1}{2} b^{x} + 3 a^{x + 1} (\frac{1}{2} b^{x})^{2} + (\frac{1}{2} b^{x})^{3} : \frac{8 a ^{3 (x + 1)} + 6 a ^{x + 1} b ^{2 x} + b ^{3 x} + 12 b ^{x} a ^{2 (x + 1)}}{8}

= \frac{8 a ^{3 (x + 1)} + 6 a ^{x + 1} b ^{2 x} + b ^{3 x} + 12 b ^{x} a ^{2 (x + 1)}}{8}

\frac{5}{13}

2 (\frac{x - 7}{2}) + 7

(- 10 x^{5}) (- 2 x)

\frac{a - b}{a + b}

e^{0.75}

What is expand (a^{x+1}+1/2 b^x)^3 ?
The solution to expand (a^{x+1}+1/2 b^x)^3 is (8a^{3(x+1)}+6a^{x+1}b^{2x}+b^{3x}+12b^xa^{2(x+1)})/8