Expand and simplify (3x+2) (x-5)

We expand this term by term.

To make sure we expand every term, I use the beak method. To do this, draw 2 curves over the equation from the 3x to the x, and then a second curve from the x to the +2.

Then draw 2 more curves, this time under the equation, from the 3x to the -5, and the second from the -5 to the +2.

You will notice the lines make an outline of a beak.

Now we are ready to multiply all of the lines.

3x * x = 3x²

x * 2 = 2x

3x * -5  = -15x

5 * 2 = -10

Now we simply add all of these calculated terms together:

3x²+2x-15x-10

We can do one step of simplification as there are two x terms:

2x-15x=-13x

This now gives us the final answer:

3x²-13x-10