What is expand (1+tan(x))^4 ?

The solution to expand (1+tan(x))^4 is 1+4tan(x)+6tan^2(x)+4tan^3(x)+tan^4(x)

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expand (1+tan(x))^4

expand

(1 + tan (x))^{4}

1 + 4 tan (x) + 6 tan^{2} (x) + 4 tan^{3} (x) + tan^{4} (x)

Solution steps

(1 + tan (x))^{4}

Apply binomial theorem:

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

a = 1, b = tan (x)

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} tan^{i} (x)

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} tan^{0} (x) : 1

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} tan^{2} (x) : 6 tan^{2} (x)

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} tan^{4} (x) : tan^{4} (x)

= 1 + 4 tan (x) + 6 tan^{2} (x) + 4 tan^{3} (x) + tan^{4} (x)

a (2 x e^{3 x} + e^{3 x} \cdot 3 x^{2}) - b sin (x) + d cos (x)

(- 4, - 2) y (- 2, - 8)

so l v e (51.64 \cdot x^{3} + 2 \cdot x - 0.9125, x)

(\frac{1}{x} - x)^{5}

(x - 2) (x + 2) (x - 7)

What is expand (1+tan(x))^4 ?
The solution to expand (1+tan(x))^4 is 1+4tan(x)+6tan^2(x)+4tan^3(x)+tan^4(x)