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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`

See also Expanding Binomials