Factoring an expression

[Angel319]

Write the expression [MATH]x^6 + x^4 + x^2y^2 + y^4 - y^6[/MATH] as a product of three factors.
(Hint: Factor separately [MATH]x^6 - y^6[/MATH] and [MATH]x^4 + x^2y^2 + y^4[/MATH].)

 

[Steven G]

So what is your question? Where are you stuck? This is not a homework service site. We expect you to solve your own problem with our help.

Did you do as suggested by the hint? Can you please post that work? Thank you.

 

[Otis]

… Factor separately [MATH]x^6 - y^6[/MATH] and [MATH]x^4 + x^2y^2 + y^4[/MATH]

Hi Angel. Are you familiar with the name 'Difference of Squares'? (That's one of the special factoring patterns.)

A^2 - B^2 = (A + B)(A - B)

We can express x^6 - y^6 as a difference of squares, by using a basic property of exponents. Let A=x^3 and B=y^3.

(x^3)^2 - (y^3)^2

After you factor the difference of squares, you'll need to continue with two additional special patterns: 'Sum of Cubes' and 'Difference of Cubes'.

A^3 + B^3 = (A + B)(A^2 - A·B + B^2)

A^3 - B^3 = (A - B)(A^2 + A·B + B^2)

When you have completely factored x^6-y^6, multiply the following before continuing with the given hint.

(A^2 - A·B + B^2)(A^2 + A·B + B^2)

If you get stuck with anything, please show us how far you got. Thanks.

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