What is expand ((x+Δx)^{(2)}+(x+Δx))/((3)) ?

The solution to expand ((x+Δx)^{(2)}+(x+Δx))/((3)) is (x^2)/3+(2Δx^2)/3+(Δ^2x^2)/3+x/3+(Δx)/3

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expand ((x+Δx)^{(2)}+(x+Δx))/((3))

expand

\frac{( x + Δ x ) ^{(2)} + ( x + Δ x )}{( 3 )}

\frac{x ^{2}}{3} + \frac{2Δ x ^{2}}{3} + \frac{Δ ^{2} x ^{2}}{3} + \frac{x}{3} + \frac{Δ x}{3}

Solution steps

\frac{( x + Δ x ) ^{2} + ( x + Δ x )}{3}

Remove parentheses:

(a) = a

= \frac{( x + Δ x ) ^{2} + x + Δ x}{3}

Expand

(x + Δ x)^{2} + x + Δ x : x^{2} + 2Δ x^{2} + Δ^{2} x^{2} + x + Δ x

= \frac{x ^{2} + 2Δ x ^{2} + Δ ^{2} x ^{2} + x + Δ x}{3}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{2} + 2Δ x ^{2} + Δ ^{2} x ^{2} + x + Δ x}{3} = \frac{x ^{2}}{3} + \frac{2Δ x ^{2}}{3} + \frac{Δ ^{2} x ^{2}}{3} + \frac{x}{3} + \frac{Δ x}{3}

= \frac{x ^{2}}{3} + \frac{2Δ x ^{2}}{3} + \frac{Δ ^{2} x ^{2}}{3} + \frac{x}{3} + \frac{Δ x}{3}

\frac{( 2 s - 2 )}{( s ^{2} - 2 s + 5 ) ^{2}}

\frac{7 ( - 2 y + 85 )}{6}

\frac{( 2 x - 7 ) ( 3 x ^{2} - 4 + x )}{( 3 x - 5 ) ^{3}}

lo g_{10} (10) x^{3} y

x^{2} + i^{3} x + i^{2}

What is expand ((x+Δx)^{(2)}+(x+Δx))/((3)) ?
The solution to expand ((x+Δx)^{(2)}+(x+Δx))/((3)) is (x^2)/3+(2Δx^2)/3+(Δ^2x^2)/3+x/3+(Δx)/3