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

1 Answer
George C.
May 8, 2016

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

Explanation:

Note the difference of squares identity:

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

So we find:

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

#(x-3)(x+3) = x^2-3^2 = x^2-9#

Then if it helps, we can use FOIL to multiply out the resulting two binomials:

#(x^2-1)(x^2-9)#

#=overbrace((x^2 * x^2))^"First" + overbrace(((x^2) * (-9)))^"Outside" + overbrace(((-1) * (x^2)))^"Inside" + overbrace(((-1) * (-9)))^"Last"#

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

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

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

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