How do you multiply $(x-6)(x+4)(x+8)$ ?

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Answer 1 · 2015-04-23T08:18:43

$(x-6)(x+4)(x+8)$

$= {(x - 6)(x + 4)}(x + 8)$

We use the Distributive Property of Multiplication or FOIL method to solve the product in the curly brackets

$= {x*x + x*4 -6*x -6*4}(x + 8)$

$= {x^2 + 4x -6x - 24}(x + 8)$

$= {x^2 - 2x - 24}(x+8)$

We again use the Distributive Property of Multiplication or FOIL method to solve the product above

$= x^2*x + x^2*8 - (2x)*x -(2x)*8 - 24*x -24*8$

$= x^3 +8x^2 - 2x^2 - 16x -24x - 192$

$color(green)( = x^3 +6x^2 - 40x - 192$

It would be a good idea to verify your answer

Take any value of x (say 6)

$(x-6)(x+4)(x+8) = (6-6)(6+4)(6+8) = 0$

$x^3 +6x^2 - 40x - 192$

$= 6^3 +6(6^2) -40*6 - 192 = 216 + 216 -240 -192 = 0$

You can try it out with a couple of more values and you will see that both expressions will always equal each other.

How do you multiply (x-6)(x+4)(x+8)(x-6)(x+4)(x+8)?