What is factor (x+Δx)^3-x^3 ?

The solution to factor (x+Δx)^3-x^3 is Δ(Δ^2+3Δ+3)x^3

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factor (x+Δx)^3-x^3

factor

(x + Δ x)^{3} - x^{3}

Δ (Δ^{2} + 3Δ + 3) x^{3}

Solution steps

(x + Δ x)^{3} - x^{3}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

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

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

Refine

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

Factor

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

= Δ (Δ^{2} + 3Δ + 3) x^{2} x

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x x^{2} = x^{1 + 2}

= Δ (Δ^{2} + 3Δ + 3) x^{1 + 2}

Add the numbers:

1 + 2 = 3

= Δ (Δ^{2} + 3Δ + 3) x^{3}

2 (x cos (ln (x)))

2^{2 x} - 2^{x + 1} + 1

4 wt + 2 w h + 6 i t + 3 ih

4 sin (3 x - 21)

5 e^{4} + 25 e^{3} - 120 e^{2}

What is factor (x+Δx)^3-x^3 ?
The solution to factor (x+Δx)^3-x^3 is Δ(Δ^2+3Δ+3)x^3