What is expand (sec(x)-1)^3 ?

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

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expand (sec(x)-1)^3

expand

(sec (x) - 1)^{3}

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

Solution steps

(sec (x) - 1)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

(2 x y - sin^{2} (x)) d x + (x^{2} + 2 y) d y

(2 x + 3 y) (4 x + 5 y)

(cos (x) e n (x) - x y^{2}) \cdot 1 - x^{2}^{- 1 + y}

\frac{2 ( x ^{5} - 12 )}{x ^{4}}

2 (- 3 - 3)

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