What is expand (9x^2+9Δx^2)Δx ?

The solution to expand (9x^2+9Δx^2)Δx is 9Δx^3+9Δ^2x^3

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expand (9x^2+9Δx^2)Δx

expand

(9 x^{2} + 9Δ x^{2}) Δ x

9Δ x^{3} + 9 Δ^{2} x^{3}

Solution steps

(9 x^{2} + 9Δ x^{2}) Δ x

= Δ x (9 x^{2} + 9Δ x^{2})

Apply the distributive law:

a (b + c) = ab + a c

a = Δ x, b = 9 x^{2}, c = 9Δ x^{2}

= Δ x \cdot 9 x^{2} + Δ x \cdot 9Δ x^{2}

= 9Δ x^{2} x + 9ΔΔ x^{2} x

Simplify

9Δ x^{2} x + 9ΔΔ x^{2} x : 9Δ x^{3} + 9 Δ^{2} x^{3}

= 9Δ x^{3} + 9 Δ^{2} x^{3}

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What is expand (9x^2+9Δx^2)Δx ?
The solution to expand (9x^2+9Δx^2)Δx is 9Δx^3+9Δ^2x^3