How do you factor the expression #x^2 - 169#?

2 Answers
Jan 10, 2016

Answer:

#(x+ 13)(x - 13)#

Explanation:

This is a difference of two squares so it factors as #(a - b)(a +b)#, where a and b are the square roots of the original expression. See proofs below.

Warning: Differences of squares only works when there is a minus between the two terms, and doesn't work if it is positive. A sum of squares can't be factored with real numbers

#x^2 - 169#

#= (x + 13)(x - 13)#, since #x • x = x^2# and #13 • -13 = -169#.

#x^2 - 169 = (x+ 13)(x - 13)#

Below are a few exercises to practice yourself. Watch out for the trick question(s) near the end!!:)

  1. Factor each expression completely

a) #x^2 - 49#

b) #4x^2 - 81#

c) #x^2 + 25#

d) #x^4 - 16#

Hopefully this helps. Best of luck in the future!

Jun 30, 2018

Answer:

#(x+ 13)(x - 13)#

Explanation:

What we have is a difference of squares, which has the form

#a^2-b^2#, where #a# and #b# are perfect squares, which factor as

#(a+b)(a-b)#

In our example, #a=x^2#, and #b=sqrt169#, or #b=13#. We can plug this into our difference of squares expansion equation to get

#(x+13)(x-13)#

Hope this helps!