How do you factor the expression #x^2 - 64#?

2 Answers
Jun 19, 2018

Answer:

See a solution process below:

Explanation:

This is a special form of the quadratic function:

#color(red)(a)^2 - color(blue)(b)^2 = (color(red)(a) + color(blue)(b))(color(red)(a) - color(blue)(b))#

Let #color(red)(a)^2 = x^2# then #sqrt(color(red)(a)^2) = sqrt(x^2) -> color(red)(a) = x#

Let #color(blue)(b)^2 = 64# then #sqrt(color(blue)(b)^2) = sqrt(64) -> color(blue)(b) = 8#

Substituting gives:

#color(red)(x)^2 - color(blue)(64) = (color(red)(x) + color(blue)(8))(color(red)(x) - color(blue)(8))#

Jun 19, 2018

Answer:

#(x-8)(x+8)#

Explanation:

Given: #x^2-64#.

Notice how #64=8^2#.

#=x^2-8^2#

Use the difference of squares property, which states that #a^2-b^2=(a-b)(a+b)#. Letting #x=a,b=8#, we get:

#=(x-8)(x+8)#