What is expand (ap(1-t)^3)/((1-t)p+tq) ?

The solution to expand (ap(1-t)^3)/((1-t)p+tq) is (ap-3apt+3apt^2-apt^3)/(p-pt+tq)

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expand (ap(1-t)^3)/((1-t)p+tq)

expand

\frac{a p ( 1 - t ) ^{3}}{( 1 - t ) p + tq}

\frac{a p - 3 a pt + 3 a p t ^{2} - a p t ^{3}}{p - pt + tq}

Solution steps

\frac{a p ( 1 - t ) ^{3}}{( 1 - t ) p + tq}

(1 - t)^{3} = 1 - 3 t + 3 t^{2} - t^{3}

= \frac{a p ( - t ^{3} + 3 t ^{2} - 3 t + 1 )}{p ( - t + 1 ) + tq}

Expand

(1 - t) p + tq : p - pt + tq

= \frac{a p ( - t ^{3} + 3 t ^{2} - 3 t + 1 )}{p - pt + tq}

Expand

a p (1 - 3 t + 3 t^{2} - t^{3}) : a p - 3 a pt + 3 a p t^{2} - a p t^{3}

= \frac{a p - 3 a pt + 3 a p t ^{2} - a p t ^{3}}{p - pt + tq}

(x - 1 + 3) (x - 1 - 3)

\frac{x - 5}{( x + 1 ) ( x ^{2} - 2 x + 1 )}

\frac{( x + h ) ^{\frac{4}{3}} - x ^{\frac{4}{3}}}{h ( ( x + h ) ^{\frac{2}{3}} + x ^{\frac{2}{3}} )}

\frac{x ^{2} + 2 x - 9}{( 1 + x ) ^{2}}

\frac{1}{( s ^{2} + 1 ) ( s ^{2} + 2 s + 3 )}

What is expand (ap(1-t)^3)/((1-t)p+tq) ?
The solution to expand (ap(1-t)^3)/((1-t)p+tq) is (ap-3apt+3apt^2-apt^3)/(p-pt+tq)