What is expand L{(t+3)^2}(s+1) ?

The solution to expand L{(t+3)^2}(s+1) is Lt^2s+6Lts+9Ls+Lt^2+6Lt+9L

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expand L{(t+3)^2}(s+1)

expand

L {(t + 3)^{2}} (s + 1)

L t^{2} s + 6 L t s + 9 L s + L t^{2} + 6 L t + 9 L

Solution steps

L {(t + 3)^{2}} (s + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = L {(t + 3)^{2}}, b = s, c = 1

= L {(t + 3)^{2}} s + L {(t + 3)^{2}} \cdot 1

= L s {(t + 3)^{2}} + 1 L {(t + 3)^{2}}

Simplify

L s {(t + 3)^{2}} + 1 L {(t + 3)^{2}} : L t^{2} s + 6 L t s + 9 L s + L t^{2} + 6 L t + 9 L

= L t^{2} s + 6 L t s + 9 L s + L t^{2} + 6 L t + 9 L

(- 2)^{5}

- \frac{( x + 1 ) ( x - 3 )}{3}

x (x^{2} + 2 x + 3)^{2}

(3 y d x + 6 d x - x d y = 0) \frac{1}{y d x}

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

What is expand L{(t+3)^2}(s+1) ?
The solution to expand L{(t+3)^2}(s+1) is Lt^2s+6Lts+9Ls+Lt^2+6Lt+9L