What is expand-5(x+Δx)^4 ?

The solution to expand-5(x+Δx)^4 is -5x^4-20Δx^4-30Δ^2x^4-20Δ^3x^4-5Δ^4x^4

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expand-5(x+Δx)^4

expand

- 5 (x + Δ x)^{4}

- 5 x^{4} - 20Δ x^{4} - 30 Δ^{2} x^{4} - 20 Δ^{3} x^{4} - 5 Δ^{4} x^{4}

Solution steps

- 5 (x + Δ x)^{4}

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

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

Distribute parentheses

= (- 5) x^{4} + (- 5) \cdot 4Δ x^{4} + (- 5) \cdot 6 Δ^{2} x^{4} + (- 5) \cdot 4 Δ^{3} x^{4} + (- 5) Δ^{4} x^{4}

Apply minus-plus rules

+ (- a) = - a

= - 5 x^{4} - 5 \cdot 4Δ x^{4} - 5 \cdot 6 Δ^{2} x^{4} - 5 \cdot 4 Δ^{3} x^{4} - 5 Δ^{4} x^{4}

Simplify

- 5 x^{4} - 5 \cdot 4Δ x^{4} - 5 \cdot 6 Δ^{2} x^{4} - 5 \cdot 4 Δ^{3} x^{4} - 5 Δ^{4} x^{4} : - 5 x^{4} - 20Δ x^{4} - 30 Δ^{2} x^{4} - 20 Δ^{3} x^{4} - 5 Δ^{4} x^{4}

= - 5 x^{4} - 20Δ x^{4} - 30 Δ^{2} x^{4} - 20 Δ^{3} x^{4} - 5 Δ^{4} x^{4}

(- 5, 1 - 65) (- 5, 8) y (- 5, - 6)

A (- \frac{1}{2}, 3) y B (4, - \frac{2}{3})

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

(16 - y) (\frac{y}{2} + 15)

(a_{1} e + a_{2} e)^{3}

What is expand-5(x+Δx)^4 ?
The solution to expand-5(x+Δx)^4 is -5x^4-20Δx^4-30Δ^2x^4-20Δ^3x^4-5Δ^4x^4