What is expand (1+tan(x))^3 ?

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

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expand (1+tan(x))^3

expand

(1 + tan (x))^{3}

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

Solution steps

(1 + tan (x))^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(1 + tan (x))^{3} = 1^{3} + 3 \cdot 1^{2} tan (x) + 3 \cdot 1 \cdot tan^{2} (x) + tan^{3} (x)

= 1^{3} + 3 \cdot 1^{2} tan (x) + 3 \cdot 1 \cdot tan^{2} (x) + tan^{3} (x)

Simplify

1^{3} + 3 \cdot 1^{2} tan (x) + 3 \cdot 1 \cdot tan^{2} (x) + tan^{3} (x) : 1 + 3 tan (x) + 3 tan^{2} (x) + tan^{3} (x)

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

\frac{( ( 3 s - 1 ) ( 2 s - 1 ) )}{( s ( s ^{2} - 2 s + 14 ) )}

\frac{s - 1}{( s + 1 ) ( s + 2 ) ( s + 3 ) ( s + 4 )}

\frac{7}{( x + 1 ) ^{2}}

\frac{2 x ^{3} - 24 x ^{2} + 71 x - 63}{( x - 4 ) ^{2} ( x ^{2} - 3 x + 3 )}

(4 x - 2 i)^{2}

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