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

2 Answers
Apr 27, 2018

Answer:

#(x^2+16)(x+4)(x−4)#

Explanation:

#x^4 - 256#

Recall; #16^2 = 256#

#:. x^4 - 16^2#

#x^2(2) - 16^2#

Recall; #x^2 - y^2 = (x + y) (x - y) -> "difference of two squares"#

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

Factoring; #x^2 - 16 = (x + 4) (x - 4)#

Therefore;

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

Apr 27, 2018

Answer:

#(x-4)(x+4)(x+4i)(x-4i)#

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)#