Put
the "distributive method" of multiplication to work. Multiply each term from the binomial times each term of the
trinomial. You can do this by using either a horizontal
method or a vertical method.
Note: FOIL will not work in
this problem.

Horizontal Method:

(x + 3)(x² + 2x + 4)

=
x³ + 2x² + 4x + 3x² + 6x + 12

=
x³ + 2x² + 3x² + 4x + 6x + 12
Group like terms.

=
x³ + 5x² + 10x + 12
Combine like terms.

Vertical Method:

x² + 2x + 4

x + 3

x³ + 2x² + 4x

3x² + 6x + 12

Line up like terms.

x³ + 5x² + 10x + 12

Add like terms.

Cubing a Binomial

Expand: (x + 3)³

If you take your time, this
problem is really
very simple.
All you need to do is multiply twice.
Multiply (x + 3) times (x + 3), and then
multiply that answer by
(x + 3). Simple!

(x + 3)³

= (x + 3)(x + 3)(x + 3)

= (x² + 3x + 3x + 9)(x + 3)
the first multiplication is done

= (x + 3) (x² + 6x + 9)
combine like terms and switch order

=
x³ + 6x² + 9x + 3x² + 18x + 27
multiply again

= x³ + 9x² + 27x + 27
combine like terms

The "distributive method"
of multiplication was used in this problem.
Note: FOIL will not work
for the second multiplication in
this problem.