What is expand 2(x+δx)^5 ?

The solution to expand 2(x+δx)^5 is 2x^5+10δx^5+20δ^2x^5+20δ^3x^5+10δ^4x^5+2δ^5x^5

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expand 2(x+δx)^5

expand

2 (x + δ x)^{5}

2 x^{5} + 10 δ x^{5} + 20 δ^{2} x^{5} + 20 δ^{3} x^{5} + 10 δ^{4} x^{5} + 2 δ^{5} x^{5}

Solution steps

2 (x + δ x)^{5}

(x + δ x)^{5} = x^{5} + 5 δ x^{5} + 10 δ^{2} x^{5} + 10 δ^{3} x^{5} + 5 δ^{4} x^{5} + δ^{5} x^{5}

= 2 (x^{5} + 5 δ x^{5} + 10 δ^{2} x^{5} + 10 δ^{3} x^{5} + 5 δ^{4} x^{5} + δ^{5} x^{5})

Distribute parentheses

= 2 x^{5} + 2 \cdot 5 δ x^{5} + 2 \cdot 10 δ^{2} x^{5} + 2 \cdot 10 δ^{3} x^{5} + 2 \cdot 5 δ^{4} x^{5} + 2 δ^{5} x^{5}

Simplify

2 x^{5} + 2 \cdot 5 δ x^{5} + 2 \cdot 10 δ^{2} x^{5} + 2 \cdot 10 δ^{3} x^{5} + 2 \cdot 5 δ^{4} x^{5} + 2 δ^{5} x^{5} : 2 x^{5} + 10 δ x^{5} + 20 δ^{2} x^{5} + 20 δ^{3} x^{5} + 10 δ^{4} x^{5} + 2 δ^{5} x^{5}

= 2 x^{5} + 10 δ x^{5} + 20 δ^{2} x^{5} + 20 δ^{3} x^{5} + 10 δ^{4} x^{5} + 2 δ^{5} x^{5}

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

(2 p + \frac{3}{4}) (2 p - \frac{3}{4})

(i)^{\frac{1}{2}}

(1 - \frac{3}{3}) \cdot (1 + \frac{3}{3})

5 l e f t (4 - a + 3 x) + (2 + a - x)

What is expand 2(x+δx)^5 ?
The solution to expand 2(x+δx)^5 is 2x^5+10δx^5+20δ^2x^5+20δ^3x^5+10δ^4x^5+2δ^5x^5