What is expand ((4a^x+b^x)^2)/4 ?

The solution to expand ((4a^x+b^x)^2)/4 is 4a^{2x}+2a^xb^x+(b^{2x})/4

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expand ((4a^x+b^x)^2)/4

expand

\frac{( 4 a ^{x} + b ^{x} ) ^{2}}{4}

4 a^{2 x} + 2 a^{x} b^{x} + \frac{b ^{2 x}}{4}

Solution steps

\frac{( 4 a ^{x} + b ^{x} ) ^{2}}{4}

(4 a^{x} + b^{x})^{2} = 16 a^{2 x} + 8 a^{x} b^{x} + b^{2 x}

= \frac{16 a ^{2 x} + 8 a ^{x} b ^{x} + b ^{2 x}}{4}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{16 a ^{2 x} + 8 a ^{x} b ^{x} + b ^{2 x}}{4} = \frac{16 a ^{2 x}}{4} + \frac{8 a ^{x} b ^{x}}{4} + \frac{b ^{2 x}}{4}

= \frac{16 a ^{2 x}}{4} + \frac{8 a ^{x} b ^{x}}{4} + \frac{b ^{2 x}}{4}

Divide the numbers:

\frac{16}{4} = 4

= 4 a^{2 x} + \frac{8 a ^{x} b ^{x}}{4} + \frac{b ^{2 x}}{4}

Divide the numbers:

\frac{8}{4} = 2

= 4 a^{2 x} + 2 a^{x} b^{x} + \frac{b ^{2 x}}{4}

\frac{x ^{3} - 36 x}{( x + 1 ) ^{2}}

(n + 2)!

(x - \frac{2}{3}) (x + \frac{2}{3})

\frac{\frac{d}{d t} ( e ( 1 - e ^{n} ) )}{1 - e}

\frac{2 x ( 1 + x )}{( 1 + 2 x ) ^{2}}

What is expand ((4a^x+b^x)^2)/4 ?
The solution to expand ((4a^x+b^x)^2)/4 is 4a^{2x}+2a^xb^x+(b^{2x})/4