Expand and simplify the trigonometric expression (2sin(x)+3)(sin(x)+2)

 Exercise

$\left(2sinx+3\right)\left(sinx+2\right)$

 

Multiply the single term $\sin\left(x\right)+2$ by each term of the polynomial $\left(2\sin\left(x\right)+3\right)$

$2\sin\left(x\right)\left(\sin\left(x\right)+2\right)+3\left(\sin\left(x\right)+2\right)$

 

Multiply the single term $2\sin\left(x\right)$ by each term of the polynomial $\left(\sin\left(x\right)+2\right)$

$2\sin\left(x\right)^2+4\sin\left(x\right)+3\left(\sin\left(x\right)+2\right)$

 

Multiply the single term $3$ by each term of the polynomial $\left(\sin\left(x\right)+2\right)$

$2\sin\left(x\right)^2+4\sin\left(x\right)+3\sin\left(x\right)+6$

 

Combining like terms $4\sin\left(x\right)$ and $3\sin\left(x\right)$

$2\sin\left(x\right)^2+7\sin\left(x\right)+6$

$2\sin\left(x\right)^2+7\sin\left(x\right)+6$

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