What is expand 5(x+dx)^4 ?

The solution to expand 5(x+dx)^4 is 5x^4+20x^3dx+30x^2dx^2+20xdx^3+5dx^4

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expand 5(x+dx)^4

expand

5 (x + d x)^{4}

5 x^{4} + 20 x^{3} d x + 30 x^{2} d x^{2} + 20 x d x^{3} + 5 d x^{4}

Solution steps

5 (x + d x)^{4}

(x + d x)^{4} = x^{4} + 4 x^{3} d x + 6 x^{2} d x^{2} + 4 x d x^{3} + d x^{4}

= 5 (x^{4} + 4 x^{3} d x + 6 x^{2} d x^{2} + 4 x d x^{3} + d x^{4})

Distribute parentheses

= 5 x^{4} + 5 \cdot 4 x^{3} d x + 5 \cdot 6 x^{2} d x^{2} + 5 \cdot 4 x d x^{3} + 5 d x^{4}

Simplify

5 x^{4} + 5 \cdot 4 x^{3} d x + 5 \cdot 6 x^{2} d x^{2} + 5 \cdot 4 x d x^{3} + 5 d x^{4} : 5 x^{4} + 20 x^{3} d x + 30 x^{2} d x^{2} + 20 x d x^{3} + 5 d x^{4}

= 5 x^{4} + 20 x^{3} d x + 30 x^{2} d x^{2} + 20 x d x^{3} + 5 d x^{4}

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

L [t^{2}] (s - 3)

(L^{t} - L^{- t})^{3}

\frac{s ^{2} + 7 - e ^{- π s}}{s ( s ^{2} + 16 )}

\frac{( x ^{2} - 1 ) ^{2}}{4}

What is expand 5(x+dx)^4 ?
The solution to expand 5(x+dx)^4 is 5x^4+20x^3dx+30x^2dx^2+20xdx^3+5dx^4