Expanding more than Two Binomials

## Expanding more than Two Binomials

Expanding more than two binomials is carried out by multiplying the binomials in steps. Multiply one binomial at a time against the expression.

Because you will be multiplying a binomial against a quadratic, it is easiest to use a table.

## Example 1

Expand (x + 3)(x -2)(x + 7)

First multiply (x+3) and (x-2)

 x +3 x x^2 3x -2 -2x -6 =(x^2 + x - 6)

Next multiply the answer (x^2 + x - 6) by (x + 7)

 x +7 x^2 x^3 7x^2 +x x^2 +7x -6 -6x -42 =x^3 + 8x^2 + x - 42

Answer: x^3 + 8x^2 + x - 42

## Example 2

Expand (x^2 + 2x - 4)(x^2 -2x + 4)

Set it up as a table::

 x^2 2x -4 x^2 x^4 +2x^3 -4x^2 -2x -2x^3 -4x^2 8x +4 +4x^2 8x -16 = x^4 -4x^2 +16x -16

Answer: x^4 - 4x^2 + 16x - 16