how does 3sin^2(x)cos(x)-2sin(x)cos(x) becomes sin(x)cos(x)(3sin(x)-2)?
To show that the expression 3sin^2(x)cos(x)-2sin(x)cos(x) can be simplified to sin(x)cos(x)(3sin(x)-2), we need to factor out the common term sin(x)cos(x) from both terms.
Starting with the original expression:
3sin^2(x)cos(x)-2sin(x)cos(x)
Let's factor out sin(x)cos(x) from each term:
= (sin(x)cos(x))(3sin(x) - 2)
Now, we have sin(x)cos(x) multiplied by the expression (3sin(x) - 2), which gives us sin(x)cos(x)(3sin(x) - 2).