What is expand 2/3 (-1+Δx) ?

The solution to expand 2/3 (-1+Δx) is -2/3+(2Δx)/3

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expand 2/3 (-1+Δx)

expand

\frac{2}{3} (- 1 + Δ x)

- \frac{2}{3} + \frac{2Δ x}{3}

Solution steps

\frac{2}{3} (- 1 + Δ x)

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{2}{3}, b = - 1, c = Δ x

= \frac{2}{3} (- 1) + \frac{2}{3} Δ x

Apply minus-plus rules

+ (- a) = - a

= - 1 \cdot \frac{2}{3} + Δ \frac{2}{3} x

Simplify

- 1 \cdot \frac{2}{3} + Δ \frac{2}{3} x : - \frac{2}{3} + \frac{2Δ x}{3}

= - \frac{2}{3} + \frac{2Δ x}{3}

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