How do you factor: #y= 2x^3 -32x #?

2 Answers
sjc
Apr 21, 2018

#y=2x(x+4)(x-4)#

Explanation:

#(1)" "#we take out the #hcfs#

y=2x^3-32x#

#hcf(2,32)=2#

#y=color(red)(2)(x^3-16x)#

#hcf(x,x^3)=x#

#y=2color(red)(x)(x^2-16)#

#(2)" "#apply difference of squares

#a^2-b^2=(a+b)(a-b)#

#y=2x(x+4)(x-4)#

Jim G.
Apr 21, 2018

#y=2x(x-4)(x+4)#

Explanation:

#"take out a "color(blue)"common factor "2x#

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

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

#"which factors in general as"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"here "a=x" and "b=4#

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

#rArry=2x(x-4)(x+4)#

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