What is expand (i2^{k-2}((-ia)^k-(ia)^k))/a ?

The solution to expand (i2^{k-2}((-ia)^k-(ia)^k))/a is (i2^{k-2}(-ia)^k)/a-2^{k-2}i^{1+k}a^{k-1}

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expand (i2^{k-2}((-ia)^k-(ia)^k))/a

expand

\frac{i 2 ^{k - 2} ( ( - ia ) ^{k} - ( ia ) ^{k} )}{a}

\frac{i 2 ^{k - 2} ( - ia ) ^{k}}{a} - 2^{k - 2} i^{1 + k} a^{k - 1}

Solution steps

\frac{i 2 ^{k - 2} ( ( - ia ) ^{k} - ( ia ) ^{k} )}{a}

Expand

i 2^{k - 2} ((- ia)^{k} - (ia)^{k}) : i 2^{k - 2} (- ia)^{k} - i 2^{k - 2} (ia)^{k}

= \frac{i 2 ^{k - 2} ( - ia ) ^{k} - i 2 ^{k - 2} ( ia ) ^{k}}{a}

Apply the fraction rule:

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

\frac{i 2 ^{k - 2} ( - ia ) ^{k} - i 2 ^{k - 2} ( ia ) ^{k}}{a} = \frac{i 2 ^{k - 2} ( - ia ) ^{k}}{a} - \frac{i 2 ^{k - 2} ( ia ) ^{k}}{a}

= \frac{i 2 ^{k - 2} ( - ia ) ^{k}}{a} - \frac{i 2 ^{k - 2} ( ia ) ^{k}}{a}

Cancel

\frac{i 2 ^{k - 2} ( ia ) ^{k}}{a} : 2^{k - 2} i^{k + 1} a^{k - 1}

= \frac{i 2 ^{k - 2} ( - ia ) ^{k}}{a} - 2^{k - 2} i^{k + 1} a^{k - 1}

\frac{z ( 65 a ^{3} b ^{5} - 174 c ^{2} x )}{1885 a ^{2} b ^{3} c}

\frac{( x ^{2} - 16 ) ( x ^{2} + 6 x + 8 )}{( x - 1 ) ( x ^{2} + 2 x - 3 )}

\frac{d ^{2} y}{d ^{2} x} (x^{2} + y^{2} = 25)

\frac{d}{d t} ((x) (a (a t^{2} + b t + c) + b)^{r (x, t)})

\frac{2 x - 4}{( x ^{2} + x ) \cdot ( x ^{2} + 1 )}

What is expand (i2^{k-2}((-ia)^k-(ia)^k))/a ?
The solution to expand (i2^{k-2}((-ia)^k-(ia)^k))/a is (i2^{k-2}(-ia)^k)/a-2^{k-2}i^{1+k}a^{k-1}