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

1 Answer
Nov 1, 2015

Answer:

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

Explanation:

Frist of all, use twice the formula #(a+b)(a-b)=a^2-b^2# to obtain

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

If you're satisfied, you can leave the expression like this. Otherwise, you can go for a full expansion, multiplying term by term, and obtaining

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