How do you multiply #(x - 1)(x + 1)(x - 3)(x + 3)#?

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Answer 1 · 2016-04-21T12:30:40

#(x-1)(x+1)(x-3)(x+3)=x^4-10x^2+9#

We can make the process a bit shorter by using the special product for the difference of sums:

#a^2-b^2 = (a+b)(a-b)#

Using that, we have:

#color(red)((x-1)(x+1))color(blue)((x-3)(x+3)) = color(red)((x^2-1))color(blue)((x^2-9))#

From here, we use standard methods for multiplying binomials.

#(x^2-1)(x^2-9) = x^2*x^2 -9x^2-1x^2+(-1)(-9)#

#=x^4-10x^2+9#