What is expand (\H(t-1)-\H(t-4))(t+1) ?

The solution to expand (\H(t-1)-\H(t-4))(t+1) is t\H(t-1)+\H(t-1)-t\H(t-4)-\H(t-4)

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expand (\H(t-1)-\H(t-4))(t+1)

expand

(H (t - 1) - H (t - 4)) (t + 1)

t H (t - 1) + H (t - 1) - t H (t - 4) - H (t - 4)

Solution steps

(H (t - 1) - H (t - 4)) (t + 1)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = H (t - 1), b = - H (t - 4), c = t, d = 1

= H (t - 1) t + H (t - 1) \cdot 1 + (- H (t - 4)) t + (- H (t - 4)) \cdot 1

Apply minus-plus rules

+ (- a) = - a

= t H (t - 1) + 1 \cdot H (t - 1) - t H (t - 4) - 1 \cdot H (t - 4)

Simplify

t H (t - 1) + 1 \cdot H (t - 1) - t H (t - 4) - 1 \cdot H (t - 4) : t H (t - 1) + H (t - 1) - t H (t - 4) - H (t - 4)

= t H (t - 1) + H (t - 1) - t H (t - 4) - H (t - 4)

\frac{3 b}{( s + 2 ) ^{2} ( s + 4 )}

\frac{( x ^{2} - 4 ) ( x + 2 )}{9 ( x ^{2 x} + 4 x + 4 )}

\frac{1 - e ^{- 2 s}}{s ( s ^{2} + 16 )}

5 cos (2) (π - θ)

\frac{50}{3} \cdot (30 - i \cdot 40)

What is expand (\H(t-1)-\H(t-4))(t+1) ?
The solution to expand (\H(t-1)-\H(t-4))(t+1) is t\H(t-1)+\H(t-1)-t\H(t-4)-\H(t-4)