# How do you factor the expression #x^4 - 256#?

##### 2 Answers

Apr 27, 2018

#### Explanation:

Recall;

Recall;

Factoring;

Therefore;

Apr 27, 2018

#### Explanation:

#x^4-256" is a "color(blue)"difference of squares"#

#"which factors in general as"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#(x^2)^2=x^4" and "(16)^2=256#

#rArra=x^2" and "b=16#

#rArrx^4-256=(x^2-16)(x^2+16)#

#"factoring "x^2-16" as a "color(blue)"difference of squares"#

#rArrx^2-16=(x-4)(x+4)#

#"we can factor "x^2+16" by solving "x^2+16=0#

#x^2+16=0rArrx^2=-16rArrx=+-4i#

#rArrx^2+16=(x+4i)(x-4i)#

#rArrx^4-256=(x-4)(x+4)(x+4i)(x-4i)#