What is expand (x+δx)^4 ?

The solution to expand (x+δx)^4 is x^4+4δx^4+6δ^2x^4+4δ^3x^4+δ^4x^4

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expand (x+δx)^4

expand

(x + δ x)^{4}

x^{4} + 4 δ x^{4} + 6 δ^{2} x^{4} + 4 δ^{3} x^{4} + δ^{4} x^{4}

Solution steps

(x + δ x)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = δ x

= i = 0 \sum 4 (i 4) x^{(4 - i)} (δ x)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (δ x)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (δ x)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (δ x)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (δ x)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (δ x)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (δ x)^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (δ x)^{1} : 4 δ x^{4}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (δ x)^{2} : 6 δ^{2} x^{4}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (δ x)^{3} : 4 δ^{3} x^{4}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (δ x)^{4} : δ^{4} x^{4}

= x^{4} + 4 δ x^{4} + 6 δ^{2} x^{4} + 4 δ^{3} x^{4} + δ^{4} x^{4}

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

lo g_{6} (x) (x - 1)^{2}

1 - (sin (A) + cos (A)) 2

(2 - 3 x) (x - 1)^{2} (x - 1 + 3) (x - 1 - 3)

x (x^{2} + 1)

What is expand (x+δx)^4 ?
The solution to expand (x+δx)^4 is x^4+4δx^4+6δ^2x^4+4δ^3x^4+δ^4x^4