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.