How do you factor #3x^4-81xy^3#?

Answer 1

Kennedy Adams

#3x(x-3y)(x^2+3xy+9y^2)#

#"take out a "color(blue)"common factor "3x#

#=3x(x^3-27y^3)#

#x^3-27y^3" is a "color(blue)"difference of cubes"#

#"which factors in general as"#

#a^3-b^3=(a-b)(a^2+ab+b^2)#

#"here "a=x" and "27y^3=(3y)^3rArrb=3y#

#x^3-27y^3=(x-3y)(x^2+3xy+9y^2)#

#3x^4-81xy^3=3x(x-3y)(x^2+3xy+9y^2)#

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Answer 2

Eva Abramson

To factor (3x^4 - 81xy^3):

First, identify the greatest common factor (GCF) of the terms, which is (3x).
Factor out the GCF: (3x(x^3 - 27y^3)).
Recognize that (x^3 - 27y^3) is a difference of cubes, so factor it accordingly: (3x(x - 3y)(x^2 + 3xy + 9y^2)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.