How do you factor # 162x^3 + 384#?

1 Answer
Jim G.
Sep 11, 2017

#6(3x+4)(9x^2-12x+16)#

Explanation:

#"take out the "color(blue)"common factor"" of 6"#

#rArr6(27x^3+64)to(color(red)(1))#

#27x^3+64" is a "color(blue)"sum of cubes"#

#•color(white)(x)a^3+b^3=(a+b)(a^2-ab+b^2)#

#27x^3=(3x)^3rArra=3x#

#64=(4)^3rArrb=4#

#rArr27x^3+64=(3x+4)(9x^2-12x+16)#

#"returning to "(color(red)(1))#

#rArr162x^3+384=6(3x+4)(9x^2-12x+16)#

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