Expand and simplify the trigonometric expression (tan(x)+15)(tan(x)-4)

 Exercise

$\left(tan\:x\:+\:15\right)\left(tan\:x-4\right)$

 

Multiply the single term $\tan\left(x\right)-4$ by each term of the polynomial $\left(\tan\left(x\right)+15\right)$

$\tan\left(x\right)\left(\tan\left(x\right)-4\right)+15\left(\tan\left(x\right)-4\right)$

 

Multiply the single term $\tan\left(x\right)$ by each term of the polynomial $\left(\tan\left(x\right)-4\right)$

$\tan\left(x\right)^2-4\tan\left(x\right)+15\left(\tan\left(x\right)-4\right)$

 

Multiply the single term $15$ by each term of the polynomial $\left(\tan\left(x\right)-4\right)$

$\tan\left(x\right)^2-4\tan\left(x\right)+15\tan\left(x\right)-60$

 

Combining like terms $-4\tan\left(x\right)$ and $15\tan\left(x\right)$

$\tan\left(x\right)^2+11\tan\left(x\right)-60$

$\tan\left(x\right)^2+11\tan\left(x\right)-60$

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