What is expand (tan(θ)-1+sqrt(2))^2 ?

The solution to expand (tan(θ)-1+sqrt(2))^2 is -2tan(θ)+tan^2(θ)+2sqrt(2)tan(θ)-2sqrt(2)+3

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expand (tan(θ)-1+sqrt(2))^2

expand

(tan (θ) - 1 + 2)^{2}

- 2 tan (θ) + tan^{2} (θ) + 22 tan (θ) - 22 + 3

Solution steps

(tan (θ) - 1 + 2)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(tan (θ) - 1 + 2)^{2} = (tan (θ) - 1 + 2) (tan (θ) - 1 + 2)

= (tan (θ) - 1 + 2) (tan (θ) - 1 + 2)

Distribute parentheses

= tan (θ) tan (θ) + tan (θ) (- 1) + tan (θ) 2 - 1 \cdot tan (θ) - 1 \cdot (- 1) - 1 \cdot 2 + 2 tan (θ) + 2 (- 1) + 22

Simplify

tan (θ) tan (θ) + tan (θ) (- 1) + tan (θ) 2 - 1 \cdot tan (θ) - 1 \cdot (- 1) - 1 \cdot 2 + 2 tan (θ) + 2 (- 1) + 22 : - 2 tan (θ) + tan^{2} (θ) + 22 tan (θ) - 22 + 3

= - 2 tan (θ) + tan^{2} (θ) + 22 tan (θ) - 22 + 3

cos (x) (x - π)

- \frac{1}{6} (x - 1) (x - 2)

tan^{2} (x) - sin^{2} (x) (cot (c) o t x + tan (x))

(1 + \frac{2 i}{n})^{3}

(8 + sin (t))^{2} + cos^{2} (t)

What is expand (tan(θ)-1+sqrt(2))^2 ?
The solution to expand (tan(θ)-1+sqrt(2))^2 is -2tan(θ)+tan^2(θ)+2sqrt(2)tan(θ)-2sqrt(2)+3