What is expand (t(2-t))*2 ?

The solution to expand (t(2-t))*2 is -2t^2+4t

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expand (t(2-t))*2

expand

(t (2 - t)) \cdot 2

- 2 t^{2} + 4 t

Solution steps

(t (2 - t)) \cdot 2

Remove parentheses:

(a) = a

= t (2 - t) \cdot 2

= 2 t (2 - t)

Apply the distributive law:

a (b - c) = ab - a c

a = t \cdot 2, b = 2, c = t

= t \cdot 2 \cdot 2 - t \cdot 2 t

= 2 \cdot 2 t - 2 tt

Simplify

2 \cdot 2 t - 2 tt : 4 t - 2 t^{2}

= 4 t - 2 t^{2}

Rewrite in standard form

= - 2 t^{2} + 4 t

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