What is expand t(x=x^1+t(x^2-x^1)) ?

The solution to expand t(x=x^1+t(x^2-x^1)) is tx=x+t^2x^2-t^2x

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expand t(x=x^1+t(x^2-x^1))

expand

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

t x = x + t^{2} x^{2} - t^{2} x

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = t, b = x = x^{1}, c = t (x^{2} - x^{1})

t x = x^{1} + tt (x^{2} - x^{1})

Expand

x^{1} + tt (x^{2} - x^{1}) : x + t^{2} x^{2} - t^{2} x

t x = x + t^{2} x^{2} - t^{2} x

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What is expand t(x=x^1+t(x^2-x^1)) ?
The solution to expand t(x=x^1+t(x^2-x^1)) is tx=x+t^2x^2-t^2x