What is expand t'F(t)(3t-7)^2 ?

The solution to expand t'F(t)(3t-7)^2 is 9t^2t'F(t)-42tt'F(t)+49t'F(t)

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expand t'F(t)(3t-7)^2

expand

t^{'} F (t) (3 t - 7)^{2}

9 t^{2} t' F (t) - 42 tt' F (t) + 49 t' F (t)

Solution steps

t^{'} F (t) (3 t - 7)^{2}

(3 t - 7)^{2} = 9 t^{2} - 42 t + 49

= t^{^{'}} F (t) (9 t^{2} - 42 t + 49)

Distribute parentheses

= t^{^{'}} F (t) \cdot 9 t^{2} + t^{^{'}} F (t) (- 42 t) + t^{^{'}} F (t) \cdot 49

Apply minus-plus rules

+ (- a) = - a

= 9 t^{2} t^{^{'}} F (t) - 42 t t^{^{'}} F (t) + 49 t^{^{'}} F (t)

\frac{32 x ^{2}}{( x - 6 ) ( x + 2 ) ^{2}}

\frac{x}{( s ^{2} + x ^{2} ) ( s ^{2} + 4 s + 13 )}

\frac{k ( s + 0.5 )}{( s + 1 ) ( s ^{2} + 2 s ) + k ( s + 0.5 )}

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

\frac{1 - e ^{- s}}{s ^{2} ( s + 1 )}

What is expand t'F(t)(3t-7)^2 ?
The solution to expand t'F(t)(3t-7)^2 is 9t^2t'F(t)-42tt'F(t)+49t'F(t)