What is expand (t-a)(\H(t-a)-\H(t-b)) ?

The solution to expand (t-a)(\H(t-a)-\H(t-b)) is t\H(t-a)-t\H(t-b)-a\H(t-a)+a\H(t-b)

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expand (t-a)(\H(t-a)-\H(t-b))

expand

(t - a) (H (t - a) - H (t - b))

t H (t - a) - t H (t - b) - a H (t - a) + a H (t - b)

Solution steps

(t - a) (H (t - a) - H (t - b))

Apply FOIL method:

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

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

= t H (t - a) + t (- H (t - b)) + (- a) H (t - a) + (- a) (- H (t - b))

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= t H (t - a) - t H (t - b) - a H (t - a) + a H (t - b)

\frac{( 8 - x )}{( x + 2 ) ^{2}}

x^{2} y^{''} (x) + x (x + 2) y^{'} (x) - (x + 2) y

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

i x (i x + 3) (i x + 6)

What is expand (t-a)(\H(t-a)-\H(t-b)) ?
The solution to expand (t-a)(\H(t-a)-\H(t-b)) is t\H(t-a)-t\H(t-b)-a\H(t-a)+a\H(t-b)