What is expand (sqrt(x)+Δx)^3 ?

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

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expand (sqrt(x)+Δx)^3

expand

(x + Δ x)^{3}

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

Solution steps

(x + Δ x)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = x, b = Δ x

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

Simplify

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

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

(2 x + 7) lo g_{10} (2 x + 7) + 3

(4 x + x y^{2}) d x + (y + x^{2} y) d y

24 (263 - 45)

\frac{( x + 3 ) ( x ^{2} - 16 )}{( 2 x + 1 ) ( 3 ^{x} + x ^{2} )}

y (x - 7)

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