Assuming one factor of x^4 - a^4 is x-a (the divisor), what is the other factor?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to notice that `x^4-a^4`  is a difference of squares and you should convert it into the special product, such that:

`x^4 - a^4 = (x^2)^2 - (a^2)^2`

`x^4 - a^4 = (x^2 - a^2)(x^2 + a^2)`

You should notice the difference of squares `x^2 - a^2`  that you may convert it into the special product such that:

`x^4 - a^4 = (x - a)(x + a)(x^2 + a^2)`

If you perform the division by `x-a` , yields:

`(x^4 - a^4)/(x - a) = ((x - a)(x + a)(x^2 + a^2))/(x - a)`

Notice that the divisor `x - a`  is also a factor of `x^4 - a^4` , hence, you should simplify by `x - a`  such that:

`(x^4 - a^4)/(x - a) = (x + a)(x^2 + a^2)`

Hence, performing the division by `x - a,`  yields `(x^4 - a^4)/(x - a) = (x + a)(x^2 + a^2).`

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